In the animation below, it appears as though Mario is jumping vertically and the Koopa shell is gliding horizontally. But actually, as you can clearly see when the background stops moving, Mario and the shell both move in circles!
(This illusion is a variation on Stuart Anstis' Flying Bugs illusion.)
So what's going on here? The first thing to note is that, although Mario and the shell are following a similar circular trajectory, they are in antiphase. Which is just a fancy way of saying that when Mario is at 12 o'clock, the shell is at 6 o'clock. The background image also follows a circular trajectory. But it goes clockwise, so the rotation of the background is opposite to that of Mario and the shell.
The crux of the illusion is that the rotations of the three elements (Mario, the shell, and the background) are aligned in a very specific way. The horizontal component of the background motion is the same as Mario's: When the background moves to the right, so does Mario. Mario's horizontal movement is therefore cancelled out, and consequently Mario appears to move only vertically. Conversely, the vertical component of the background motion is matched to that of the shell. Therefore, the shell appears to move only horizontally.
This illusion is a very salient demonstration of how we use background information to make judgements about positions and movement. We don't perceive the actual movement of Mario and the shell, we perceive their movement relative to the background.
Simple as that! But quite striking, I think.