What causes the spokes of a Wagon Wheel to "move"(rotate) in the opposite direction of the Wagon Wheel itself?
This happens when the wheel is observed as an image through a projector or with light shining on it that is periodically blinking. What you are seeing is essentially the additive effects of two periodic functions, the first is the period of the light flicker and the second is the period of the wheel rotation.

So, if the wheel is rotating at a frequency that is evenly divisible by the frequency of the light, then the spokes appear to be standing still. If it is rotating faster, then they are appear to be moving in one direction. If it is rotating slower, then it appears to be moving in the other.

Under household lighting, the light pulses are at 60 Hz. The frame rate of movie cameras is usually 24 Hz.