Having just read vireo's explanation of torque steer above, I feel compelled to offer a slight expansion of the explanation in case anyone out there needs as much additional puzzling over it as I did. The key points to note are the following:
• At rest, the tires (we can assume) sit on a contact patch which is an approximate rectangle as the weight of the car compresses the bottom of the tire against the road
• The tires in question are the drive tires in a front wheel drive car, i.e. they're designed to pivot (steer)
• When they do rotate, they don't rotate around the middle of that contact patch. They rotate around the point where the kingpin axis intersects the road, labeled in the lower diagram with a line from the word 'offset'
So, let's assume you begin to accelerate. The mass of the car resists moving, while the wheel tries to pull it forward. If the wheel above existed on its own, imagine that the inner end of the axle in the diagram above is fixed (by the car's inertia) while you pushed hard at the back side of the tire. What would happen?

The tire and wheel would start to move forward. However, they would be restrained from doing so by two forces - one, the axle (i.e. the mass of the car) and two, by the resistance of the pavement (the contact patch). We can pretty much ignore the former, because axles are designed (well, most of them) not to swing forward and back. However, look carefully at the second restraining force.

Now, there is a patch of friction (let's call it a rectangle for simplicity) which is the contact patch. The wheel is designed to rotate around the kingpin axis, which is not in the exact center of the contact patch! As a result, the forces of resistance (backwards) on the wheel at the contact patch will not be equally distributed around that pivot point. What happens?

Bingo. The wheel rotates around its pivot point. The car steers. Since the kingpin axis is usually inboard of the center of the tire due to the vagaries of having to put mechanisms at the hubs of car wheels, the tires will almost always steer inward.

Now, this is normally not noticeable, because as the writeup above notes, the front wheels of most well-designed cars are mirror images - so the forces acting on the car cancel out whenever it accelerates. That, however, is in a perfect world, and we all know how often one of those rolls around. There is the problem of simple maintenance - the kingpin axes on each side of the car may not be identical; the tires may not be identically worn, etc.

There are also situational factors to consider. One side of the car may be downhill from the other, thus shouldering more of the car's weight and distorting the tire into a wider contact patch. This is why FWD cars will torque steer suddenly when you hit a bump - usually, bumps hit one wheel at a time, not two, and the wheel whose tire is flattened out more (or which simply remains on the ground when the other loses grip) will exert a greater steering force than the other. Boom, torque steer.

Finally, some car designs make the problem inherently worse. If the engine is mounted such that the driveshaft is aligned with the car's long axis, then all of the pistons will be exerting force on one side of that driveshaft during acceleration - and the engine will have a tendency to try to rotate in its mounts, pressing one side of the car down during acceleration.

A final note - well, reiteration, really. Rear wheel drive cars don't really torque steer because their steering tires are not being driven by the engine - although they do have the same contact patch/kingpin axis dislocation. The distance between the two, by the way, is sometimes called the scrub radius, because if the car is stopped, that distance of the contact patch will 'scrub' across the ground when the steering wheel is turned rather than the wheel rotating in place. Something similar can happen if a RWD car hits a bump in a mode which has the front tires pressed firmly to the ground and under forward or backward stress- cornering or braking, for example. This, naturally, is called bump steering.

SharQ points out that some 4WD or AWD cars can suffer from torque steer as well. He also notes something important which I should have mentioned originally, which is that modern stability control/traction control systems, hooked to clever differentials, can do much to counter torque steer. If the system detects torque steer, it can cut power to the wheel on the outside of the turn momentarily. This will counteract the effect.

Transitional Man chimes in with a bit of trivia, noting that torque steer gets worse as horsepower increases and as a result while the lower classes of GT racing (GTL) have FWD cars in the top slots, this is not true once you get above 250 HP (GT-3).