I use Microsoft Paint and CoffeeCup GIF Animator. I always save as Bitmaps, then use the GIF Animator to convert it to GIF (not always just animation). I also use ReaConverter Pro to convert to other formats, since Paints messes up the colour usually if you try to save as soemthing other than Bitmap.
^ All FREE! CoffeCup is a 14 day trial, but even after 14 days it still works. It'll say your trial expires in a negative amount of days. O_o
Sadly, I have nothing special (I have Maya. It's a 3D animation program, but I don't think that's what you want). I want Photoshop and a scanner and hopefully a tablet, but I've never gotten around to it.