No one has mentioned Sherlock Hound? Shame. Basically Lupin III with dogs and steampunk and a vague connection to the works of Sir Arthur Conan Doyle. The whole thing is legally available on Youtube with a pretty fantastic dub.
The closest thing to furry anime I can find is Tetsuwan Birdy, after they reach outer space. Pretty much every Alien race they encounter save for Birdy's, is a furry. Dino-anthromorph, dogs, cats, insects, lizards, frogs.