The world is three dimensional and most animations/models are more realistic if they involve three dimensions. It often does not seem that more difficult to program the distributions and motions, but it is definitely more difficult to display the images.
The simplest is to show objects which are closer to the viewer as overlapping objects which are further away. This animation of helical movement uses this method.
A more complicated way is to make use of the brain's ability to make an internal 3 dimensional image by combining the view from right and left eyes. On the computer, there seem to be three ways to make an artificial stereo image that don't require a lot of extra optics / electronics. One involves the viewer to fuse two images together, either by crossing eyes or going "wall-eyed". Another involves the use of red green stereo pairs and requires red / green stereo glasses. Another involves using a mirror placed in the middle of two images. This stereo animation lets you see the three different ways and to change some of parameters for making a stereo image, especially the stereo angle.
Three dimensional rotations: This animation shows a starfish oocyte being rotated in space. The axes of rotation are fixed in space, and are thus relative to the viewer. This animation shows the x y and z axis of an object being rotated in space. These rotations are relative to the frame of reference of the object, rather than that of the viewer. This animation shows a mobius strip being rotated in space (relative to its own axes) and also shows how the mobius strip intersects with planes parallel to the monitor screen.
Color stereo by fusing images (i.e., not red green glasses): brownian, ropes 1 - 2, variable viewing angle, rotation of 3 axes (using euler angles), rotation of a starfish oocyte, (red / green rotation of oocyte)
Stereoviewer - pictures from 2007
Arbitrary rotation of 3 axes