What is the voltage of an average carpet static shock? Can you make it lethal? I think I heard somewhere that it was in the thousands of volts, but it had extremely, extremely low amps. Could you somehow transform the current to make it larger or something? Or does the equation of volt*amp apply, making the overall power still merely an annoying sting?
 A: The energy in a typical static charge from walking across a carpet is too low to kill a human. It may be a few milliJoules.
The energy available is approximately Voltage x Charge. The current that passes through your body depends on that voltage divided by the effective resistance of your body (including any clothing, shoes and other material in the discharge path).  But the time this current flows is very small because the amount of charge is very small.
Since energy is a conserved quantity, there is nothing you can do with the available voltage or current that will make a more dangerous amount of energy available.
A: 
I think I heard somewhere that it was in the thousands of volts, but it had extremely, extremely low amps.

Well, you heard wrong.
Electrostatic discharges from humans can be thousands of volts and several amps.
The reason it doesn't kill you is because it's a very small amount of electric charge, and so the discharge only lasts for a very short duration.
Background:

ESD tests with an intervening metal object are referred to as "hand/metal" tests. They are meant to represent the general case of a hand with any interposed metal object such as a ring, watch, bracelet, tool or key. The hand/metal discharge has become a de facto worst-case standard for ESD-testing of high-quality industrial and consumer equip­ment. Peak currents that result from it are typically an order of magnitude higher than discharge currents from a hand alone, without an intervening metal object.
Evidently a smooth, round electrode of moder­ate diameter causes far higher currents with far shorter rise times than a sharp electrode

Some results:

Peak currents don't differ greatly, ranging from 19 to 29A, as electrodes are changed from sharp (Fig. 5(a)) to rounded (the 1-2 mm ball of Fig. 5(c)).
Once again the ring [on finger] is at least as great a threat as an ESD electrode, as an 8 mm dia­meter ball tip. Peak currents at this 4 kV level range to 23A


Classification of ESD Hand/Metal Current Waves Versus Approach Speed, Voltage, Electrode Geometry and Humidity
Here's another for comparison:


Fig. 2. Discharge current of a human holding a 5 cm key at 1 kV, arm bent.

ESD: Waveform calculation, field and current of
human and simulator ESD
So if discharges from a finger are an order of magnitude lower, we can guess that they peak around 3 A.  You can see that these peak currents only last a few nanoseconds, though.
(Yes, people intentionally shock themselves many times at thousands of volts for science.)
A: A hospital-type defibrillator provides capacitor-discharge with hundreds of joules per pulse.  Carpet/doorknob sparks are quite a bit less:
Carpet shocks:

*

*750V, 0.04mJ - Spark threshold, visible in darkness

*4KV, 1.2 mJoules - Winter doorknob spark, small snap, little pinprick

*7KV, 3.7 mJoules - Fairly nasty spark, louder snap.  Ouch.

*35KV, 100 mJoules - Highest measured spark: northshore Alaska winter, vinyl truck seat.

*Taser, tens/hundreds of mJoules, repeating pulse

*100KV,
half a joule - VandeGraaff machine with chain of children connected

Defibrillator designers say that the "danger zone" for producing fibrillation is in the range of joules or few tens of joules.  Lower than that, and the impulses cannot trigger fibrillation in normal hearts.  And far higher, instead we get "defib" or "cardioversion" effects where the pulse momentarily overrides the heart's natural pacemaker.  Note that this applies to external defib, as with paddle electrodes applied to skin.
Can we make it lethal?  Yes, just stab a piece of coathanger into your chest muscles, and apply the spark directly!  ;)  That's "internal defibrillation" using implanted electrodes.  One of the early heart researchers managed to kill himself in just this way, by applying quite small pulses to his chest electrodes, but with pulses adjusted to be in the center of the phase/amplitude "lethal window" in his heart's QRS waveform.  If you doorknob-zap an implanted chest electrode, probably you won't die the first time, but don't repeat the experiment over and over, because eventually you'll accidentally miss the lucky conditions.
The old trick with the VandeGraaff machine and the row of schoolkids holding hands is probably unwise.  If the last kid in the chain happens to have a serious undiagnosed heart condition, the big zap from the stored charge is near the lower threshold of actually causing harm.
A: To get a spark in air (under standard conditions) you need a potential of approximately 3kV per millimeter of distance.  If you see a spark just before your finger touches a doorknob, you can use that to roughly estimate what the voltage difference was.
Electric charge flows (very briefly) between your finger and the doorknob, until the potential difference between them is no longer enough to overcome the resistance.
For electricity to be lethal, you need the current to flow through a vital organ, like your heart.  The datasheet for a human being is probably pretty long:  humanoids have complex topology and different types of tissue have different resistances.  Dry skin has a much higher resistance than many of the wetter squishy bits on the inside.
If you where to reach out to two different doorknobs that had a large potential different between them, then your body would be a conductor (with moderate resistance).  Given that your skin has pretty high resistance, the current would likely flow along the outer layers for your skin.  But if the current persisted for more than a split second, your body might dump moisture out your sweat glands.  That moisture drops the skin's resistance, making the route through your insides much more attractive.
People who work with high voltage are taught (among other things) to where rubber soled shoes and to work with only one hand.  The idea is to reduce the chance of completing a circuit with a large portion of your body.  If you accidentally "short" a circuit with your hand, you might get a nasty current running through your fingers and hand (see Electroboom's YouTube channel for examples), but that's better than having it flow through the trunk of your body where the life support systems are located.  (Electrodes on Taser are arranged to send current through a short span rather than across the core.)
A: It must be mentioned that there are a lot of variables at play here. 
The amount of voltage generated by the static shock varies on the method used to obtain the static shock and the materials used. This post is an interesting look at the situation.
The resistance of a human is very hard to quantify and varies depending on conditions such as moisture, gender, body type, body part, path the voltage takes, and what they're wearing. The resistance of a person's skin is between $1,000Ohms$ and $100,000Ohms$ (though some say it's around $5,000 - 15,000Ohms$), the internal anywhere from $300-1,000Ohms$. We can practically consider a person's total resistance as the resistance of the skin going in, the internal resistance and the resistance of the skin going out in in series going, the total resistance is the sum of all the resistance. Thus $R_{total} = R_{skinIn)} + R_{internal} + R_{skinOut}$.
The current (what actually kills people) is based on these, determined by Ohm's Law, which says $I = V / R$.
Although around $40,000V$ is usually enough to be fatal, it's also worth noting that while current is based on the voltage, humans have lived through being touched by absurd amounts of voltage and lived. The most recorded while still living, according to Guinness, was $340,000V$ given to Harry F. Mcgrew who came into direct contact with a transmission line. The usual static shock is around $500V$, maxing out around $21,000V$.

With that being said, from most sources I can find on Google, the general consensus says around $0.1-0.2A$ can kill a human. But I believe that it is only when there is a sustained current, though I can't find how long it needs to be sustained on average (I suppose they don't ever test it because we don't want people to die).
A relevant equation that may explain the need for a sustained current is $Q = I * T$, where charge is equal to the current multiplied by the time it's supplied. If $T$ (the time) is very small, as is the case with static shocks, the total charge is small, almost regardless of the voltage applied.
Using the data we have so far, in the case that it's most likely to kill someone is with a low resistance (perhaps it's a fit guy who is wet and the current doesn't go through much of the other person's body), we get $I = V / R = 21,000V / 2,300Ohms = 9.1A$, but this seems absurdly high. Also keep in mind that this is applied for a tiny amount of time, likely a fraction of a tenth of a second.
In the least likely (and probably more accurate given we don't ever see this happening) case to kill someone using the data so far is $I = V / R = 500V / 100,000Ohms = 0.005A$ applied over the same time, a fraction of a tenth of a second.
The real value may be somewhere between these two, but I bet it's more towards the second than the first.
