Using the GIF file format, you can save an image containing multiple frames, thereby making an animation which a few here have taken advantage of by making their signature in this way. Assuming you're not going for a terribly complicated animation, a basic tutorial (such as this one for Gimp) about GIF animation should be simple enough to follow. If you're going for something more complex, a minute or two with a search engine and a couple keywords will probably yield the results you're looking for.
Unfortunately, GIF files do have downsides, mainly a major loss of quality in images with a large variety of colours due to a rather limited colour palette (256 colours, if I'm not mistaken) and there being only one level of transparency possible, thereby producing different results than those desired when more than one level of transparency is in use (such as a border fading into transparency or something similar in the animation). For those reasons I personally prefer to use an online service like the one Sprolf linked (or, for those that have the means, one's own website with a script described somewhere else on the forums which I can't be bothered to look up right now), but to each his own.
THEY TOLD ME I COULD BE ANYTHING SO I BECAME A SIGNATURE PLS HLP