Well, I for one used my good ol' Image Ready CS when I animated the text on my avatar two years ago, but there's probably better options than that one ...
Other than that I think it's possible to use GIMP as well, same goes for the later versions of Photoshop (I believe it's from Photoshop CS3 and above they fused Photoshop and Image Ready into one, but someone can correct me if I'm mistaken. I may have used Photoshop CS3 rather much in high school, but it was never for animations. And as far as I recall things it works to make animations I saw something regarding that in my Photoshop CS5 - but I honestly only use it to edit my photos in, so I haven't played around enough in it yet even though I got it in sort of Christmas/Birthday present two years ago), Flash and then there's probably a lot more.
Speaking of animations, I'm going to dig my own gave if I make my new avatar as I have imagined it (Cour flying around in a circle, sort of, it will be tiny artwork as hell and I'm not that good with pixel art. Or him just flying into the picture, flapping with his wings and then flying out and keep it going like that in an endless loop). Because I feel like it's time for a new avatar after two years with the same. xD