I was inspired by this animated avatar from free-avatars.com:
Is it possible to use an animated GIF as an avatar on gravatar.com? I couldn't get it to work, but maybe someone else knows a hack.
AFAIK, this isn't possible.
Every time I upload an image, gravatar's system forces me to "crop" it. I believe they just extract the first frame from an animated image.
Check this blog post, you can see in the comments where people are complaining about this issue and png transparency too.
EDIT: Since there's a bounty for this question, here is an another quote from their official blog answering to a user asking the same thing (emphasis is mine):
Thunderm00n Says: September 3, 2008 at 2:31 pm
Hey there! Nice work, but why don`t you accept moving gifs or why we have to resize our avartas (just use a type of width and height attribute, min-height/width should be 80px max-height/width should be 120px) but its a great work. Keep on!
...which is answered:
apokalyptik Says: September 3, 2008 at 6:35 pm
(...) @Thunderm00n — It was a conscious choice not to accept animated images. On the whole most people don’t like them, and it can seriously detract from the look and feel of a site. Since we (all) are guests on peoples web pages we do our best to play nice with the other kids while we are there.