Well, Guren Lagan has characters with animalistic features, but all the ones with noticable animal features are badguys. Sure, there's that one Opossum-Eyed character, but as much as I heart opossums, I wouldn't have guessed he was part Opossum if they didn't tell me. ...Infact, they didn't. My dad had to tell me. ...But, it's imensly popular anyway, although it's just another anime about mechs. ...Oh well, moving on.
Someone mentioned Outlaw Star. While I agree that it's a very good anime, there's not one I could consider a furry in that show except for maybe that lizard guy from that one episode (Who, thank heavens, ISN'T evil, and ended up having his life save by the main characters) but other than him, no real furries. Aisha would really count more as a Neko than a furry.
But, now that I mentioned the lizard guy, he is also in a spinoff of Outlaw Star known as Angel Links. ...But I haven't seen that one, so I can't judge.
Can't think of any, really. I think it would be cool, though, if there was an anime where a race of big green guys, possibly with outrageous hair, tried to take over a world of furries. Kind of like a Furry VS Troll anime. ...Although I don't think that will ever happen.