Zeeman's Paradox states that a drawing in perspective looks realistic from many perspectives, even though it should only look right from one. It's thought that this is because we still perceive it as a drawing of a 3D space rather than a real 3D space, so our brain believes it.
Some interesting ways to fake 3d
2D layers layered on top of each other over and over again (although I guess this is close to 3D?)
One point perspective / reversed perspective?
3 images - shifting perspective on mouse rollover?