Relmstein has an interesting post up about how players develop their identities with the classes they play, and while he marks it as players connecting with the various classes they choose, I actually see more of an effect on me, the player-- when I play with my Shaman in World of Warcraft, I'm more measured, careful, and helpful, and when I play my Rogue, I tend to do a lot more ganking, cheap tricks, and sneaky stuff. My Shaman would never run up to a flag in Arathi Basin without support, because that's his thing-- he supports others with totems and helps groups. But my Rogue loves sneaking off to a flag by himself, hopefully with a clothie there that he can sap or gank.
In exactly this way, classes can help the playerbase form communities and connections of their own-- you start to identify with and support those of the same class around you. Players specialize in one class, and grow more and more familiar with and attached to it. A straightforward skill system (like that in EVE Online) doesn't have that-- you still have races, but no one identifies with the traditional class roles. Miners may stick together, but when everyone can mine, that doesn't mean as much.
And new games can learn from this, too-- we've already seen some great class ideas come out of Warhammer, and there's no doubt that if those are implemented as well as they appear to be, we'll see players stepping up to identify with the roles in that game as well.