In TV and cinema movies, the spoked wheels of fast-moving vehicles such as cars and wagons sometimes appear to rotate 'backwards'. This phenomenon is known in the scientific literature as the 'wagon wheel effect', for obvious reasons. Why does it occur?
Its origin lies in the discontinuous nature of frame-based animation. The frames in the movie are successive snapshots of the rotating wheel, taken at regular time intervals. If the wheel rotates through only a small fraction of the distance between neighbouring spokes in-between frames, then the nearest frame-to-frame match for each spoke is in the correct, forward direction, so the wheel appears to rotate forwards. On the other hand, if the wheel rotates faster so that its frame-to-frame rotation covers most of the distance between neighbouring spokes, then the nearest frame-to-frame match for each spoke is backwards (because the spoke behind has nearly caught up), so the wheel appears to rotate backwards.
In the demonstration the wheel turns one revolution at a slow speed (each spoke moves one-quarter of the distance between spokes from frame to frame), and one revolution at high speed (each spoke moves two-thirds of the distance between spokes from frame to frame). The red spot shows that the true frame-to-frame rotation of the wheel is always clockwise, but notice that at the faster speed the wheel appears to rotate backwards (given by the 'backwards' displacement of one-third of the distance between spokes).
The wagon wheel effect is an example of a sampling artifact called aliasing. It is debatable whether the effect should be classified as an illusion, since any motion-detecting system would be prone to it given discrete samples (frames) of rapid motion. There are claims in the scientific literature that the wagon wheel effect can also be seen in natural visual scenes, but these claims probably confuse two separate phenomena, with different explanations.
See:
Finlay, D., Dodwell, P. Caelli, T. (1984) The waggon-wheel effect. Perception, 13, 237-248.
Kline, K., Holcombe, A. O., & Eagleman, D. M. (2004). Illusory motion reversal is caused by rivalry, not by perceptual snapshots of the visual field. Vision research, 44(23), 2653-2658..
Purves, D., Paydarfar, J. A., & Andrews, T. J. (1996). The wagon wheel illusion in movies and reality. Proceedings of National Academy of Sciences USA, 93(8), 3693–3697.