I recommend checking out The Animation Alphabet, made by 4th and 5th graders (source of the GIFs above.) There's something simple about the setup that's really quite perfect, and something about the slowness of the looping animations... amazing. Also check out the rest of the GIFs, featuring more Paint animations and some stop motion stuff, made by Mr. Wampole's students. (Especially the stop motion Mini Movies at the very bottom.) (Found via Squeaky From, which has cool links but seems to be down right now.)

Mrs. Alyce Jenks' Second Grade Web Pages also have some exciting simple GIF animations made by kids. I think the new versions of KidPix let you do animations? Not sure. More kid art here and here, and also see Travis Hallenbeck's amazing Paint and bitmap link collections.