Please use silent HTML5 videos instead of animated GIFs wherever possible. They are much more bandwidth- and CPU-efficient. This site allows you to automatically upload/convert animated GIFs into that format: http://gfycat.com/ The links allow you to see the animated GIFs as well, if viewer's device doesn't support HTML5.
One nice thing about GIF is that the format is not patent-encumbered. Same goes for MPEG-1.
WebM seems to avoid all the problems related to patents (http://en.wikipedia.org/wiki/WebM).