The most obvious one that comes to mind is Power Wolf. Other than that, I can only think of specific songs, like TMBG's "Mammal," "The Lady and the Tiger," or "Dog Walker." Perhaps Prokofiev's Peter and the Wolf might count, as well as the countless FNAF tribute songs. Oh, there's also a handful of folk songs by S.J. Tucker, "Cheshire Kitten," "Were-Owl," "Alligator in my House," "Heartbeat" and "Mama Dragon" (although that last one is more about hanging out with an old woman than an actual dragon).
So, what about it? Know any bands dedicated specifically to animals?