I have an animated GIF that illustrates an answer, but I don't know whether the constant animation would be disruptive or noisy on the site's normally static pages. How do people feel about such images?
It's a widely-supported format but it has poor compression, so I would make sure that the file size is not too large for low-bandwidth users. I think an animated GIF would be a great way to add flair to an answer. It would be annoying in excess, but I've never seen a single animation or video inlined here (why not?).