The Sims is a pretty fun game and it usually works wonders for girlfriends. Otherwise, some "light" RPGs like Jade Empire, Mass Effect or such might also be good since they focus a lot more on storyline than level/skill progression. She can always upgrade to the more heavy RPGs later if she warms to the genre.
Alternately try some of the newer adventure/investigation games, like the CSI or Sherlock Holmes games and what not, women generally like a good mystery so if she fits the demographic they might be a hit and they don't require too much of the PC either.
But seriously, if she's not a gamer there's a good chance you're wasting your time with PC games, get her a DS instead, that's what I did for my girlfriend. She doesn't use it that often, but when she does it's hours at a time. Almost like a real gamer
Edit: Black & White or Black & White 2 might also be interesting for her, a blend of pet-simulator and strategy god game. Also Fable, although only Fable 1 is released for the PC.