If we're counting animated animal heros too, mine would have to be Feivel from An American Tail and the sequel, Feivel Goes West. Even though they were animated, they dealt with some pretty serious issues, like racism and police states. I remember identifying strongly with Feivel, because he was tiny and his living situations were percarious.
As a young child, my parents were pretty nuts, and I was in and out of different living situations regularly. It was hard for me to identify strongly with the other children at school, because their lives were so different than mine. They had so much stability: two loving parents, permanent bedrooms, not living in womens' shelters. We just didn't have much in common.
The fact that he was a mouse (and a really tiny one, at that) really spoke to me too. As a kid, you don't have much power over what happens to you. It can feel a lot like being near the bottom of the food chain, just like a mouse.
But Feivel made me feel normal. Because the story dealt with a transient population that was desperate but hopeful, I felt like I could connect. Its funny, I never really thought about how much I identified with those movies as a kid, but I really did.