OP,Jim_Callahan said:Start with two-player games. Couch co-op (e.g. Borderlands), pass-the-controller (e.g. Rayman Legends, Mario, Dark souls) and versus (Soul Calibur, League of Legends) games are all solid starting points, just make sure it's something where you can physically be in the same room and involved in the game at the same time.
This isn't a sinister plot to hook your SO on video gaming unwittingly, it's more the basic bloody common courtesy to acknowledge that part of wanting to share someone's hobbies is an implicit request to actually spend time together. If you give her a random single-player game and tell her to go off an play it you're _dismissing_ her, which besides being rude probably means your relationship countdown timer has started since finding a better SO than you probably isn't difficult at that point.
I thought I'd highlight the good post so you don't have to dig through the conceited pseudo-hidden insults. Next time just don't state the gender of the person you want to introduce to your hobby. People here have a tendency to snap at that sort of thing and attack you if it's a woman.
Though honestly, you don't even need to go the extra mile and get your hands on coop games (though some the good ones like Rayman have already been named). Just pick a title you thought was great and wouldn't mind playing again and start a new game with her, passing the controller. It's about spending time on the couch together doing something fun. I started gaming with my sister like this and we played God of War (the entire trilogy) of all things. The games are great, if goofy, overly manly and kinda sexist but it doesn't really matter if the point is spending time with someone you like, right?