Are there any good online animal breeding games

If you mean browser-based, there's lots. I personally love Furry Paws, Wajas, Howrse, and Felisfire. There are tons more that I can't remember off the top of my head though.

Also, I think I'll throw it out there that Wolfquest and Feralheart are good games too. They are free to download, but they may not be what you are looking for. Hope this helps. :)