I don't currently have a favourite animal story, but I do remember reading Babe when I was younger. I remember really enjoying it at the time (even the movie) and I think I still might have the book on my childhood bookshelf now after all these years!
I read that one as a kid too and loved it. I think it's by Dick King Smith. I liked quite a few of his, Harry's Mad was a good one (about an parrot), and Dodos are Forever (instead of being killed and eaten by sailors, dodos escape to a more remote island to live in peace).