Polar Bears would fit better into the Barbarian catergory, IMO, given that they're the biggest species of bear alive today and kill pretty much anything that isn't a female bear in heat. Grizzlies would make better hunters/trappers given that they're melee fighters that sneak around in forests and aren't batduke crazy enough to run around trying to tank everything. I'm assuming that Panda Bears are monks, because of course they'd be monks, and sun bears would be mages, because those guys look magical as hell, yo. Or maybe they'd be healers, because they've mastered the art of honey.

Spectacled bears would make great necromancers, on account of the fact that they always wear spooky voodoo makeup. Sloth bears would be good diplomats because they only eat bugs. Then again, Pandas are vegetarians (or scavengers, sometimes) but they would obviously be better at mauling the crap out of things. Maybe Sloth Bears would make good bards, on account of the fact that they have big ears...

Koala bears, being the smelly, despicable little gits they are, would obviously be the rogues in this situation, and raccoons, since they're distantly related, would be like gnomes... But that's already been sorted out in a way that makes slightly more sense. Sounds like it'd be fun, though. If I had the time...