Here are four cool animated GIFs by Fairy Suryana's Animated GIFs Gallery, a dragon by Boingdragon, a Quake III Arena icon, and a cool animated gif I found on the web of Felix the Cat (pacing back and forth, clearly thinking about a math problem), but I don't know who to give credit to for it:

A cool animated GIF of the cycloid x = r(t - sin(t)), y = r(1 - cos(t)) made by Maple.

An animated GIF showing the transformation of a helicoid to a catenoid made by Maple.

Another animated GIF, the cycloid running inside a circle made by Maple.

Another cool animated GIF of two tori made by Mathematica.

Links back to:
Alex Feingold's Webpage,
Department of Mathematical Sciences,
Binghamton University.