Is gravity just electromagnetic attraction? Recently, I  was pondering over the thought that is most of the elementary particles have intrinsic magnetism, then can gravity be just a weaker form of electromagnetic attraction? But decided the idea was silly.  
But I then googled it and found this article. Is this idea really compatible with other theories as the article mentions? Is there any chance of this proposition being true?
 A: I'd like to add mainly to Frederic Brünner's and Anna V's answers.
Let's begin with, as Frederic does:

Sunlight does not point back to the sun’s true center of gravity, whereas gravity always points back to the sun’s true center of gravity.

and

And if it propagated at the speed of light, gravity (like sunlight) would not point back to the sun’s true location; and as a result the planets would drift away from the sun and leave the solar system.

Precisely these arguments that your paper proposes have a long, long history of having been thoroughly studied, beginning with the great Laplace. See the Wiki discussion of the speed of gravity, in particular its summary of Laplace's thoughts on the matter and also this contemporary "review" from the original Usenet physics FAQ. Before general relativity, you could indeed argue that the planet orbits would not be stable with a finite lightspeed.
After General relativity is accounted for, guess what? The orbits are STILL unstable!! And this is exactly what is observed!. I'm being slightly mischievous here, because the effect on the Earth's orbit is fantastically small: Earth radiates about 200 watts of gravitational radiation. See the "power radiated by by orbiting bodies" section in the Gravitational Wave Wiki Page. So the instability is not going to show a perceptible difference in orbit any time soon! But there is an astronomical system which allows us to experimentally check the instability and that is the Hulse-Taylor binary system: this is a binary star system which has been carefully observed and measured since its discovery in 1974 and the observed spin down carefully compared with the spindown foretold by General Relativity (one calculates, by GTR, the gravitational wave power emitted). GTR exactly matches observation here. Moreover, early this year, direct observation of gravitational waves in the early cosmos is thought to have been made by the BICEP2 experiment as frozen ripples in the CBR.
So there is a great deal of evidence directly amassing for finite speed propagtion of gravitation. And that's before one looks at the theoretical argument against infinite gravitational speed propagation made by special relativity and the thoroughly experimentally tested notion of Lorentz invariance.
Lastly, let me copy Aaron Dufour's excellent comment here lest it should be deleted:

[It's] Worth noting that falling off like $1/r^2$ is a generic property of things that propagate in 3 spatial dimensions; anything else would imply energy being regularly gained/lost along the way.

and let me add to it as follows. If we go back to Laplace's simple model, where he assumes Newton's inverse square law (which, as Aaron says can be construed as a property arising in 3 spatial dimensions) and simply adds a retardation, but if we do it in a way that is Lorentz invariant in freespace, we find again that the orbit instability is much smaller. Interestingly, what you now have is the theory of Gravitoelectromagnetism, which is precisely analogous to Maxwell's equations. So here you have the full "magnetic" and "electric" laws arising simply from the  $1/r^2$ property of three spatial dimensions and then requiring the laws to be Lorentz invariant. So you would expect electric/magnetic like equations that at least roughly describe utterly unrelated phenomenonse, which is an even stronger version of Aaron's argument. Incidentally, if we note that the universal gravitation constant corresponds to $1/(4\pi\epsilon_0)$ in Maxwell's equation, then the Gravitoelectromagnetism version of the orbital instability, i.e. of the Larmor formula is:
$$P = \frac{2}{3} G^3 \frac{m_e^2\,m_s^2}{r_e^4\,c^3}$$
with $m_s$ = Sun's mass = $2\times10^30{\rm kg}$, $m_e$ = Earth's mass = $6\times10^24{\rm kg}$ and $r_e=1.5\times10^{11}{\rm m}$ I get about $3{\rm GW}$ radiation. THis sounds much more significant than the GTR loss but it would still take of the order of $10^8$ times the age of the universe for the Earth to spiral into the Sun. Gravitoelectromagnetism is falsified by the Hulse-Taylor binary. The difference is essentially that GTR only allows quadrupole and higher order radiation sources, not the much more energetic dipole radiation that Gravitoelectromagnetism (and Maxwell's equations) allows.
Footnote: Actually, we don't quite quite get Lorentz invariance with Gravitoelectromagnetism even though the equations in freespace are Lorentz invariant. It turns out that $(\rho_g,\,\vec{J}_g)$, the analogue of the current density four-vector from Maxwell's equations, is not a four-vector in GTR but merely an incomplete representation of the stress energy tensor $T$,
A: Short answer: No.
Long answer: Nooooooooooooooooooooooooooooooooooooooooooooooooooooo.
Moral of the story: Gravity and EM are two very different things that look similar to some people because they both fall off like $\frac{1}{r^2}$. Be careful what you trust. When someone makes a claim like that, check their references. If there are no references, ignore it.
A: No, gravity, first, is not a force, it is a manifestation of spacetime curvature. One can derive Maxwells equations from the Einstein field equations and the divergence-free property of the Einstein tensor, but they are fundamentally different. Of course, one can show that both theories are geometrical in nature though. 
A: The answer to the question is no.
There are several logical mistakes and flawed arguments in the article; I will comment on a few: 

Sunlight does not point back to the sun’s true center of gravity, whereas gravity always points back to the sun’s true center of gravity.

Gravity always "points" in a direction consistent with the curvature of spacetime at the position the object feeling it is located. A change in curvature corresponding to a moving source does not propagate instantaneously. As such, the actual position of the source does not have to agree with its apparent position.

And if it propagated at the speed of light, gravity (like sunlight) would not point back to the sun’s true location; and as a result the planets would drift away from the sun and leave the solar system.

This is a claim that cannot be backed up by actual calculations. 

Sir Isaac Newton’s inverse square law of gravity is essentially identical to Charles Coulomb’s inverse square law of electromagnetic attraction

Just because two concepts are similar, that does not mean that they are one and the same. The fact that both Newton's and Coulomb's laws share the $1/r^2$ behaviour proves nothing.

Millikan was neutralizing the force of gravity (creating anti-gravity), by using a battery and two metal plates to create an electrical force that was equal and opposite to the gravity force. If Millikan could neutralize the force of gravity by opposing it with a simple electrical force, this can be considered evidence that gravity is a simple electrical force of classical physics… Millikan’s oil drop experiment shows that it is possible to create artificial gravity in space, and that it is possible to create zero gravity on earth.

The only thing this proves is that the principle of superposition of forces works: two equal but opposite forces cancel each other, resulting in zero net force. This says nothing about the nature of the forces in question. 

In any case, it is necessary to understand that gravity can be described as a simple electromagnetic force of classical physics, in order to understand anti-gravity.

There is no evidence for anti-gravity and therefore no need to explain it.
A side remark: there actually are serious attempts to unify gravity and electromagnetism, most notably Kaluza-Klein theory. Even though there exists no experimental evidence for the latter, the theoretical concepts developed in the context of this approach are of great importance to modern physics. 
A: I agree with the previous answers that the cited blog article is naive and superficial.  But then all great ideas have humble beginnings.
Along similar lines of thought a respected scientist called Walther Ritz (http://en.wikipedia.org/wiki/Walther_Ritz) developed a sophisticated model of electric forces in 1908. He indicates that his model explains gravity as a small net effect of positive and negative electrical fluxes emanating from neutral atoms.  He produced equations for gravitational attraction which can be tuned (by selecting an appropriate value for an empirically-determinable factor) to account for the anomalous perihelion precession of Mercury and other astronomical, orbiting objects ( e.g. planets, asteroids, binary stars).
It is not clear to me exactly how Ritz's gravitational equation is derived from his model. Ritz's model is considered defunct by the mainstream physics establishment.  It is sometimes classified as an emission theory or ballistic theory and as such has the appeal of not requiring us to bend space or time to explain gravity.
Other respected scientists who considered (and published on) whether gravity might have an electromagnetic origin were Zollner, Mossotti, Lorentz, Gans, Wacker, Coster & Shepanski. An excellent historical account is provided in the book by Roseveare (http://www.amazon.co.uk/Mercurys-Perihelion-Verrier-Einstein-publications/dp/0198581742) .
A: First: I see two issues with this question:


*

*Will we ever know what gravity is? All we have are observations and theories. So the question should rather be: can gravity be explained with electromagnetic forces?

*What is "electromagnetic attraction"? Since the blog talks about negative charge and positive gravitons, it probably refers to "electro-static attraction". So even more precisely the question probably should be: can gravity be explained by electro-static attraction?
Now having a more precise question, let's try to answer it. There are a lot of differences between gravitation and electro-static attraction:


*

*electro-static attraction can be easily shielded, whereas shielding gravity seems to be a lot more difficult, if not impossible.

*if gravity was an electro-static force with negative masses, why would it not repel negative charges?


These obvious contradictions are not addressed in the blog. So using electro-static attraction as an explanation for gravity does not seem to work.
A: One can hand wave a lot of "theories" that sound logical. It is called "science fiction". There is a series of books by Terry Pratchett where he imagines a whole universe with different physical laws including magic. He makes it sound so logical, and two books have been written about "the science of Diskworld". Fun.
Before the ubiquitous use of mathematics into describing nature , history is full of "scientists" postulating various theories to explain observations , from the time of Artistotle all the way down to turtles on turtles. Since Newton's time physics has taken a huge leap. One cannot talk of a "theory" without solid mathematics behind it.
A blog article with a lot of statements of this that and the other, if it does not refer/link  to mathematical modeling, or contain mathematical modeling is not worth the mental effort, at least a physicist's mental effort since there are so many intriguing and possibly correct and relevant new physics papers all the time.
There exist proposals with mathematical formulations that are off the beaten track of physics. Of the ones that are not obviously crack-pot ( incoherent) some of them can easily be falsified by wrong use of mathematics or data,  some of them are set aside because they are not mainstream, and maybe sometime they might be justified by new experiments or observations . The blog entry you give a link, for does not belong to the latter case.
A: Gravity is the weakest force we know.  However a force is NOT acceleration - a force acting on a mass causes a change in the mass's momentum - THAT is associated with acceleration.  Gravity itself is still somewhat undefined - it is associated with space-time curvature, but is thought to be explainable by a wave function - as are most quantum effects - however, a gravity wave has yet to be detected.
