In the past (up to sometime near the end of 2005) users were allowed to use animated gifs as avatars. This ended when there was a sudden wave of really distracting and obnoxious flashing, gaudy avatars. Rather than make a long list of what is an isn't acceptable for animated avatar usage and then forcing the staff to monitor and police their use it was decided that they would be banned altogether. Those users who had appropriate animated avatars at the time were allowed to keep them and so you may see a small number of them floating around the forums. If/when those users decide to change their avatars they will not be allowed to replace the current animated gifs with another animated avatar but will have to choose an regular non-moving picture like the rest of us.
Honestly, can you concentrate on information with animated avatars like these next to/above the posts and possibly worse?
EDIT: In case anyone is wondering I just did a Google search and found a site that allowed them and linked a few examples from their site here in this post. These were never used by any Ubuntu Forums members as far as I can remember...those that ended the fun were far worse.
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