What systems do you have? I'm assuming your girlfriend is a non-gamer since you're looking for suggestions for something to get her into gaming. I'd say the LittleBigPlanet games are really fun, and my fiancee likes those. Super Mario Galaxy is a very fun game, and I've heard good things about Viva Pinata on 360. Also, don't forget about the classics, like Mario, Zelda, Pac-man, anything that's fairly simple but fun.