I think Chewbacca is one of the best mainstream examples of how to make a non-human race interesting and not just a regular person in a funny hat.
Chewie is the only wookie we ever see, and he doesn't look like a human at all. He has a simple anthropoid frame that most of us are familiar with--he's basically Bigfoot. He doesn't speak English at all, but somehow everyone understands him perfectly. You might say he acts like a big, brutish human... but not really. It's very clear that there's something animal-like about his behavior. His strong sense of smell is referenced a few times; he roars like a beast occasionally; he has unrestrained fits of rage, in fact he doesn't seem to be in control of his own emotions; and his strength is clearly super-human (does a regular person rip someone's arms out of their sockets when they lose?) At other times, he has an almost dog-like skittishness complete with wimpering. But we, the audience, are never confused by his intentions or emotions, and we sympathize and relate with him.
I'm not saying elves and dwarves should be this way--those races fit a different role, that of exaggerrated human personality archetypes. But certainly beast-like or totally inhuman races could take a lot from Star Wars.