SWG vet here, playing LOTRO, loved EVE's massive player contributed lore, disappointed that the Warcraft lore wasn't central to WOW, and looking forward to SW:TOR -- so, um, yes, it's important to me.

Games with rich lore create an environment where some basic level of RP isn't forced. You know what a hobbit burglar is likely to be like, and tend to fall into it a bit. You know what a Bothan spy might do or say, and you crack on it sort of casually.

Too many hard core RPers are stilted, but the sort of natural theater games that emerge in high lore environments helps immersion and adds a dimension of humor and fun to any MMO.