I'm suggesting that gif images could be disallowed in posts, signatures (sigs) and in pictures (avatars). (I see no problem on the occasional smiley.

)
The reason is that it's easy to annoy other people with them (like the sigs done by Presentiment and his alias).
If gif images are used as static images, then they could be converted to any other format, like png that has no loss of quality. But whenever gif images are used as animations, then it's easy to abuse.
If an animation is required to make a point, a member may post a link to it without showing it in the post (or, perhaps, post a link to a video instead).
I know that this suggestion would be more in time if I remembered it a couple of weeks ago, but I still think it's useful (now and then I bump into old posts near gifs).
Am I forgetting some situation where gif images are useful in posts, sigs or avatars?