Why is the charge naming convention wrong? I recently came to know about the Conventional Current vs. Electron Flow issue.
Doing some search I found that the reason for this is that Benjamin Franklin made a mistake when naming positive and negative charges.
There is even this little comic about that http://xkcd.com/567/
My question is, how can a naming convention be wrong?
Perhaps I don't understand what is the actual mistake here, I don't know. But I don't see how a naming convention could be wrong or right. There is no right and wrong about that. It could've been any other name, like charge A and charge B.
I'll appreciate anyone can help me understand what is wrong in all this.
 A: It's not a mistake, and conventional current is not wrong or backwards.
Electric current is often thought to be a flow of electrons, but this is wrong.  Electric current is a flow of electric charge. Charge can be positive (protons) or negative (electrons), and both types of charged particles can and do flow in electric circuits:


*

*In metal wires, carbon resistors, and vacuum tubes, electric current consists of a flow of electrons.

*In batteries, electrolytic capacitors, and neon lamps, current consists of a flow of ions, either positive or negative or both (flowing in opposite directions)

*In hydrogen fuel cells and water ice, current consists of a flow of protons.

*In semiconductors, the current can consist of holes, which are not quite the same as an absence of electrons.


(The Hall Effect can be used to show whether a charge carrier is positively charged and flowing in one direction, or negatively charged and flowing in the other.)
When a Lithium-ion battery discharges into a load, for instance, there is no electron flow in the battery, but there is still a current flow:

(Source: Center for Sustainable Nanotechnology)
If you considered only the electron flow, your calculations would be wrong.  You need to consider the net flow of charge, no matter what the charge carriers.  Conventional current abstracts away the different charge carriers and represents all of these different flows as a net flow of (positive) charge, simplifying circuit analysis.
Conventional current is not the opposite of electron current, so if they were defined to flow in the same direction, it would be even easier to confuse them and go through life misunderstanding what current is.  Electron current is a subset of conventional current.  Conventional current combines the effects of electron, ion, proton, and hole flows all into one number.
Wikipedia agrees:

In other media, any stream of charged objects may constitute an electric current. To provide a definition of current that is independent of the type of charge carriers flowing, conventional current is defined to flow in the same direction as positive charges.

The labeling of one polarity of charge as "positive" and the other as "negative" is totally arbitrary.  It could be done either way and everything would still work out the same.  Franklin didn't choose wrong; he just chose. Labeling protons as negative and electrons as positive wouldn't change anything.  It might actually make things more confusing, as described in Ben Franklin should have said electrons are positive?  Wrong.

If Franklin had instead chosen the electrons to be positive, then we might never confront the real problem. If electrons weren't negative, we'd easily ignore our misconceptions, and we'd end up with only an illusion of understanding. Yet also we'd still have all sorts of niggling unanswered questions caused by the misconceptions. Fortunately the negative electrons rub our noses in the problem, making our questions grow into something far more than just "niggling!"

A: Have you ever played the sliding-15 puzzle?  There are fifteen sliding pieces, numbered 1 to 15, arranged in a 4x4 grid.  It has one "hole" where there is no piece.  You can move any piece adjacent to the hole into that space.

. 
As you play the game, what is moving: the numbered pieces, or the hole?
Technically speaking, you are moving the numbered pieces.  They are the electrons, the physical objects that move around.  You can even get them to move in a complete path (a closed circuit).
But if you have played this game for enough time, you quickly realize how important the hole is to the strategy of the game.  A skilled player can move the hole anywhere he wants, and the hole can even move around in a closed circuit.  The hole represents the absence of electrons, and can move around just as the electrons themselves can.  In semiconductor theory, we even officially call them "holes" and treat them like a particle, even though they're not.
Whichever way you count, there is something moving.  In electricity, we call this "charge".  Ben Franklin called it "electric fire" (see below).
Notice that whatever move you make, there are always 15 numbered pieces and 1 hole.  We say that this is conservation of charge, and was discovered by Franklin (see below).  As long as we are counting or adding things, it makes sense to make one kind of charge positive and another kind negative.  How shall we assign which is which?
The problem is that there has never been -- and never will be -- a device which can see electrons or holes.  They're just too small and too fast.
As @endolith furthermore points out, there are many things other than electrons that can flow to produce electric current.  Nonetheless, physicists like to choose conventions.

Franklin asked several of his English colleagues for books, to establish a scientific library in America.  In early 1747, the English naturalist Peter Collinson sent Franklin a glass tube along with a shipment of books, with directions on how it was being used in electric experiments.  Apparently, physicists thought it was great fun to rub the tube and give each other shocks.  How fun!
On May 25 1747, Franklin wrote a letter back to Collinson, first thanking him for the gift, describing some of the experiments he had performed with it, and then explaining his conclusions.
Franklin described his construction of a simple electroscope, electrifying it with the tube, and then de-electrifying it with a nearby needle.  Franklin concluded that there is some kind of "element" that is being "drawn off or thrown off".  He also noticed a glow when these experiments are performed in the dark, "like that of a Fire-Fly or Glow-Worm".  Franklin therefore called it "electric fire", which we now call charge.  He made a case that this is a new chemical element (to join earth, water, air, and fire).
He then described several other experiments, but his interpretation of the following experiment is the most important:

We suppose as aforesaid, That Electrical Fire is a common Element, of which every one of the three Persons abovementioned has his equal Share before any Operation is begun with the Tube. A who stands on Wax, and rubs the Tube, collects the Electrical Fire from himself into the Glass; and his Communication with the common Stock being cut off by the Wax, his Body is not again immediately supply’d. B, who stands upon Wax likewise, passing his Knuckle along near the Tube, receives the Fire which was collected by the Glass from A; and his Communication with the common Stock being likewise cutt off, he retains the additional Quantity received. to C, standing on the Floor, both appear to be electrised; for he having only the middle Quantity of Electrical Fire receives a Spark on approaching B, who has an over-quantity, but gives one to A, who has an under-quantity.
If A and B touch each other, the Spark between them is stronger, because the Difference between them is greater. After such Touch, there is no Spark between either of them and C; because the Electrical Fire in all is reduced to the original Equality. If they touch while Electrising, the Equality is never destroyed, the Fire only circulating.
Hence have arisen some new Terms among us. We say B (and other Bodies alike circumstanced) are electrised positively; A negatively: Or rather B is electrised plus and A minus. And we daily in our Experiments electrise Bodies plus or minus as we think proper. These Terms we may use till your Philosophers give us better.
Benjamin Franklin, Letter to Peter Collinson, May 25, 1747.  Emphasis added.

Franklin had discovered the conservation of charge.  In particular, he claimed that his "electric fire" only circulated, was never destroyed, and remained in equality of amount.  As the electric fire came from the glass rod, it made sense to him that objects gaining electric fire were positively charged.
Glass is one of the most triboelectrically-positive substances; only polyurethane (not yet invented) and human skin and hair are more so.  Had Collinson instead sent Franklin a rod of sulfur -- which is triboelectrically-negative -- it is likely that we would be talking about positively-charged electrons today.  I find it poetic that "electric fire" can be made from "brimstone".
Franklin was somewhat right about "These Terms we may use till your Philosophers give us better."  Indeed, it was an Englishman (physicist J. J. Thomson) who discovered that the actual particles moving in a circuit -- which he named "electrons" -- are negatively-charged.  Unfortunately, even though something "better" came along, the convention stuck.

Returning to the original question, why is the convention "wrong"?  The most common charge carrier (the electron) flows in one direction, but the direction of charge current is expressed in the opposite direction.  The opposing directions create confusion among learners: it is not intuitive, it is confusing, learners often apply the wrong direction (or ignore direction), and it frustrates learners.  When you are learning electricity, it is thus "wrong".
There are times when it is better to use electrons, and other times when you should use current.  Just as the sliding puzzle has times when you want to move a numbered piece, and other times you want to move a hole.  A skilled practitioner knows which one to apply, and doesn't even think about the difference.
A: Sign conventions aren't "wrong", but they can be misleading.
For example, we could re-define work done in a gravitational field so that escaping earth's gravity well would require negative work. That's an equally valid convention, but we associate positive work with effort, so reversing the convention would hinder our physical intuition for no discernible benefit.
Are there cases where intuition might be misleading? Sure; in orbital mechanics, negative work can make you go faster. But that doesn't mean we should reverse the convention just because some people have the misconception "positive work makes you go faster".
For changes in oxidation state, the existing sign convention on charge is "wrong" in the sense of misleading. When an atom gains electrons, it is said to be "reduced" because its oxidation state has gone down.
This is misleading terminology rooted in a misleading convention. Admittedly, the terminology is not misleading for "reduction" involving loss of a proton, but for most atomic interactions it works against physical intuition. For example, ions generally increase in effective radius when reduced.
Students find this so unintuitive that they try to remember it by silly mnemonics like "OIL RIG" ("oxidation is loss, reduction is gain").
Same thing for current: "CCD" is a mnemonic for "cathode current departs", even though most of the time the charge carriers responsible for the current aren't physically departing from the cathode.
Yet those same students don't need a mnemonic to remember the sign for work done against the earth's gravitational field, nor for work done on charges of the same sign.
A: (Someone resurrected this oldie in the queue, so just to be a contrary voice...)
Ben Franklin did get it wrong. He had just developed a remarkable new theory of electricity in which positive (+) and negative (-) had specific and accurate meanings, and he was unable to apply the two labels in the way he intended.
In Franklin's time electricity was thought to be composed of two fluids, "vitreous" and "resinous", that annihilated each other when they came into contact. Franklin's clever idea was to realize that the two-fluid theory was redundant, and that a single fluid flowing through metals would suffice. This led him directly to an analogy with water pressure or air pressure, in which a single fluid flows from the end of a pipe that has positive (+) pressure, and towards the end with negative (-) or vacuum-like pressure. 
The problem was that Franklin had no way to separate the fluid from the metal to tell which way it was moving. He could make sparks, sure, but the fluid (electricity) moved so incredibly fast that nothing accurate could be discerned from watching them.
It was only with the invention decades later of the Crookes tube that it became possible to tell the direction of flow of this mysterious electrical fluid, specifically by watching the shadows it cast on the inside of an empty tube. Only then was it realized that the fluid that Franklin postulated was moving from the "negative" pressure side (-) to the "positive" pressure side, (+). But it was already too late. Decades of papers and textbooks using Franklin's theory and conventions had already been written, and it would have been a nightmare to attempt to flip the convention at that point.
We now call these particles of electrical fluid "electrons," and they do indeed behave very much like the fastest and most nimble fluid imaginable. For the most common way to convey this fluid, via metals, it is the negative terminal of a battery that creates a positive pressure (or voltage) to push the fluid outward, and it is the positive terminal that creates a negative pressure to pull the electrons back in.
(This similarity also explains why using analogies with water pressure to explain voltages and electrical flow can be a lot more insightful than one might expect. Both really are examples of fluids under pressure, even if the terminology is different and the analogy is incomplete due to electrons having the ability to do things that material fluids cannot.)
So, bottom line: Franklin clearly would have labeled his own choice an error if he had had access to better data, so I think we can too.
A: Benjamin Franklin's charge convention isn't "wrong" in the sense that it leads to physically incorrect answers, but it is "bad" in the sense that it requires dealing with unnecessary minus signs that wouldn't be there if the electron were assigned positive charge.
In my opinion, this problem is the most serious not in the context of current flow, but in elementary particle physics.  All the deconfined elementary fermions in the Standard Model have the same electric charge, and it would be much more natural to assign the "matter" particles positive charge and the "antimatter" particles negative charge, but unfortunately under the current convention it's the other way around.  This leads to huge sign headaches - so bad that halfway through Srednicki's QFT book, he actually redefines $e$ from the electron charge to the proton charge, making it really annoying to compare results from before and after that point.  (Of course, we could instead reverse the conventions for which particles are "matter" and which "antimatter," but under that convention the vast majority of the observable universe would consist of antimatter, which would be an even worse convention.)
A: This just a convention that arose (I think) in the 19th century before the existance of electrons had been established. There is no special significance to it.
In $p$-type semiconductors it's possible to model the current flow as the motion of positive holes, and these travel from the positive pole to the negative pole. However it's still really electrons that are moving, and you'd struggle to interpret current flow in metals using this model.
A: Central to this discussion is a common and widespread misconception:  the wrong idea that electric current is a flow of electrons, and that flows of positive charge are impossible.
Nope and nope.
Only in metals is an electric current a flow of electrons.  Protons can flow, and so can ions of both polarities.  The type of charge-carrier depends on the type of conductor: metals, electrolytes, ionized gases.   So, Franklin may have been "backwards" about way metals conduct a charge flow.  But he wasn't wrong about proton conductors and PEMs used in solid-electrolyte fuel cells.  Franklin was also wrong about battery acid and neon signs, where the moving charges have opposite polarities and flow in opposite directions.  In Franklin's terms, electrolytes contain two (or more) kinds of 'electric fluid,' not just one.
In fact, when you get shocked by a HV power supply, no electrons flow through your body.  The voltage impressed across your flesh produces a flow of the ions commonly found in your tissues: positive sodium and potassium ions, and negative chlorides, each polarity of ions flowing in opposite directions.  How then can we describe the amperes which are electrocuting you?!  Easy.  Just use Conventional Current.  That's what it's for.  (Hint: ammeters measure conventional current.  They do not report the percentages of positives and negatives drifting in opposite direction within the circuit.)
It's really quite amazing how many authors seem to believe Franklin's discredited one-fluid theory of electricity, or believe that electric currents are somehow "made out of electrons."
Conductor examples:
Metals - yes, electrons
Semiconductors - electrons in two energy bands (lower band is vacancies or 'holes')
Plasma - electrons, positive ions, negative ions (if Hydrogen plasma, then H+ bare protons are part of the current.)
Distilled water - protons (H+ ions) and OH- ions, no electrons
Battery acid - protons (H+ ions) and SO4- ions, no electrons
Oceans - Na+ ions, Cl- ions, some H+ and OH-, no electrons
Human flesh - Na+ ions, K+ ions, Cl- ions, many misc ions, no electrons
I suspect that WW-2 military training manuals are partly to blame for this situation.  For instruction of technicians, their authors concentrated on metal wires and vacuum tubes, and based their concepts on the over-simplified (wrong) idea that "electricity equals electrons," and that all positive charges were really just a case of missing electrons.
A: This is a common question and the answer is related to the fact that electric current is defined simply as the flow of electric charge.  Thus, it is an abstract current since electric charge is a property, not an entity.  Electric charge must be "carried" be something.
The direction of flow of positive charge is taken to be the direction of electric current.  Thus, a flow of negative charge contributes to an electric current in the opposite direction.
Electron current is the flow of electrons and, since electrons have the property of negative electric charge, an electron current is necessarily a flow of charge, i.e., an electric current (in the opposite direction of the electric current).
But, it is often the case that electric current is due to the flow of other charged entities besides electrons.  For example, within the electrolyte of a battery or within a plasma, the flow of charged ions contribute to the electric current.
A: Electricity is a manifestation due to electronic movement, which are negatively charged. 
But quite some time ago when this was not known, franklin proposed to call the deficiency of electrons as positive, and excess of electrons as negative; which is followed now!!! which eventually resulted in electronic charge to be known as negative!!!
Poor electron now has to live with the negative charge it was thrusted upon by Franklin.
As a matter of fact, in electrical terminology, current flows from positive terminal to negative terminal; while physically electrons flows from negative terminal to positive terminal. So, now due to that mistake by Franklin we have to call electric flow as reverse of electron flow!!!
I too wish it was the other way round, life would have been a bit more simpler!!
A: Positive charges attract negative charges.
The same goes for a positive potential (a negative charge wants it's potential to be as high as possible). So the electron flows from the -pole to the +pole increasing it's potential in the proces.
You could see the positive pole as a positive charge that's trying to attract the electon.
Or to follow the approved answer:''It's because we defined the charge of an electron to be the negative charge that these conventions mix up.'' If we were to switch all of the negative charges to positive ones and the positive to the negative ones, then the current and electron flow would coincide. That's simply a matter of convention.
A: The naming of the two types of electricities is not wrong and it cannot be a matter of human's convention at all.
(in this answer I will use the words “plus” and “minus” instead of “positive” and “negative”)
“Plus” is the effect towards outside (expansion, blowing, explosion, yang), “minus” is the effect towards inside (contraction, suctioning, implosion, yin). For example, the act of inhaling is plus, because our chest expands; the act of exhaling is minus, because it reduces in size.
From the history of electromagnetism it is known that Benjamin Franklin (1705-1790) is the man who was the first to introduce the terms “positive” and “negative”, i.e. “plus/minus” in the field of electric­ity in the middle of the 18th century. Previously, the different types of electricity had been called “vitreous” (meaning “glass”) and “resinous” (meaning “amber”), since the glass and the amber were the most often rubbed objects to produce the opposite electricities. At the time when Franklin gave his contribution, people had actually spoken of two types of electric fluids; however, Franklin argued that there is only one electric fluid, and the excess and the shortage of it in the objects he called “plus” and “minus”. He said that bodies in normal condition have medium amounts of this fluid and are there­fore neutral. When two objects are rubbed against each other, one allegedly transfers a part of its fluid to the other and thus the first becomes minus-, and the second object plus-electrified.
It remains a mystery how this type of thinking resulted in the glass electricity being called “plus”, and the amber electricity “minus”, although it has been recorded that Franklin is the man who assigned the plus to the glass, and the minus to the amber electricity.
That these things (i.e. plus and minus in the electricity and in the magnetism) are not arbitrary, I have a proof which I call an ultimate proof. A proof is ultimate when we perceive the truth immediately (directly, unmediated) with our senses, in this case, with our eyes.
If we rotate the discs of a Wimshurst machine by turning the crank manually to the right in a dark room (the most noticeable results can be seen at night in a room with a little exterior street light entering it), and if we do this for at least 10-15 seconds to let the eyes get used to the feeble light, we will notice that the horizontal quadrants emit a light flicker, whereas the vertical are completely dark. On turning the crank to the left the flicker relocates to the vertical quadrants, whereas the horizontal ones now remain dark. Looking even more attentively at the scene, we will notice an essential qualitative difference between what happens in the left and the right quadrant (i.e. the upper and the lower one when the crank is turned to the left). The flicker in one horizontal quadrant is directed from the metal sectors outwards, in the other one inwards. In other words, in the left quadrant the metal sectors are dark and the flickering light glows around them, but in the right quadrant the metal sectors are illuminated and around them it is dark.

The metallic sectors in the image are drawn as a whole, and not individually, because the light phenomenon appears as a whole; more precisely, as two wholes, one left and one right, and not individually in the sectors.
The electricity of the left quadrant (picture on the left) is the same as the vitreous electricity; the electricity of the right quadrant is the same as the resinous electricity. I will not explain how this is determined, because this answer will become much longer (you can check it out here https://newtheories.info). So, if Benjamin Franklin has determined what is positive and negative about electricity, he did it right.
If we fill the middle of a ring magnet (taken out of a small loudspeaker) with iron filings, then we tap the magnet to allow the iron powder to freely take its shape, a difference between the one and the other side becomes clearly visible. At the pole which points North a form of blowing is evident (as if we put the lips forward), and at the pole that points South a form of suction (as if we put the lips inwards). Hence, the plus-pole with an effect outwards is the magnetic South pole of the Earth, and the minus-pole with an effect inwards is the magnetic North pole of the Earth.
The electric wind blows de jure and de facto from the plus- to the minus-pole of the battery through the connecting wire. But I will explain this in another answer.
P.S. What I mean with "electric wind", you can read here https://www.quora.com/What-is-meant-by-electric-wind-What-are-some-examples/answer/Mitko-Gorgiev
