In general I find most animated avatars annoying and distracting. If everyone had good taste, it would be different, but I would be afraid we would very quickly see too many that were were just terrible. Now that said, I would support an "animated avatar weekend" once a year. It would be something many would look forward to and plan for. Such events can be community builders as members share their expertise and creativity in preparation for the "event". I could see it as a showcase event that is anticipated and enjoyed by many.
I would set up categories and allow members to vote on winners in each category. Winners would get a "small badge" for their sig or "location".
Categories:
Civ related
OT themed (religion, politics, evolution, etc.)
Most annoying
Most subtle
Most original
I'm sure there are other good ones.
I think that this site should have general and forum specific "holidays" when usually non permitted activity is allowed under controlled circumstances. This could be one of them.