Try some casual stuff first, maybe Puyo Puyo or Rock Band, and ease her into it with some simple platformers ( LittleBigPlanet, Super Mario Galaxy), and if she gets into those, pace yourself and slowly introduce other genres, even ones you aren't into. ( To each gamer their own in gaming) Try leaving brutal shooters out of it if you can ( Left4Dead, Half Life, Modern Warfare, etc.), but if you must introduce her, PORTAL is always a fun one to play.
Just remember to pace slowly, and not to show her too much at once. And unless she's into the stuff, leave survival horrors out of it, the Silent Hills especially.