GIMP for Windows is completely free. It's also overkill for just animating GIFs, but it will do the trick.
If you haven't done a lot of graphics work, it's probably not the easiest thing to use, but you just have to create an image where each layer is a frame of your animation and then save it as a GIF. At that point, it will give you some options (how long a delay between frames, whether or not to loop indefinitely, etc...)
http://www.gimp.org/windows/