Why do wheels on a car sometimes appear to be rolling in the opposite direction?

Answer 1

First of all, note, that if the wheel had an ideal plain surface, without spinners, or any other "special" areas on it, you would not be able to see it spinning at all - there just would not be any changes to register, that would indicate any motion to you.
You know the wheel is spinning because it has special points, that your eyes can fixate on and follow their movement. If you see the spinner pointing straight up one moment, and slightly to the left the next, your brain concludes that the wheel is spinning counterclockwise.
But it could also be that the wheel is spinning clockwise, only so fast that between those two moments when your eyes got fixated on this particular spinner, it had made almost the whole circle - the picture in your brain will look identical to that when the whell is spinning the other way, but much slower.

Answer 2

Only in the movies or on TV, because it is a stroboscopic illusion caused by the frame rate for those moving picture systems. That is because moving pictures are really just a bunch of still pictures, called frames, taken at a fast rate, like 30 every second. If the wheel takes just slightly less time to make one complete revolution than the time for the movie to go from one frame to the next, then each subsequent frame shows the wheel rotated slighty back from the previous frame. Play these frames at full speed and it looks like the wheel is turning backward.

Answer 3

When the rotation of the wheel is fast enough, you eyes/brain are no longer able to see the entire wheel. At that time you start to "see" pieces of the wheel instead of the whole thing. As your brain translates these pieces back together they will appear to spin in the opposite direction.

Answer 4

"spinners" give that impression.