Again, depends on what platform and what genre, but as a girl, this is what I enjoy playing with my Beau.
Dungeon Defenders, as it's been mentioned plenty of times. To me the perfect combo has been a squire/wizard or wizard/monk combo, still haven't been able to work in the huntress yet :/ but finals have kinda gotten in the way to. It's a great little tower defense and can introduce her to that genre very nicely (I've honestly been looking for other titles to play with my bf in this genre although I've tried to steer clear before).
Borderlands can be fun, but I don't know about as a newbie. I basically learned how to play fps on the pc with Borderlands and at first, that wasn't very fun, for me or for my bf, and I'd been playing fps for a while on the ps3 at this point (well okay, a few months). I'm sure you can figure out which combos would work best for you, but by the end we were kickin' it with a Lilian/Mordecai combo
Army of Two on the ps3. Now the 2nd one wasn't nearly as much fun, but we've played through the first one a bit and that's how I learned to play 3ps. Granted before this I'd avoided shooters like the plague so I sucked, but it was forgiving enough on easy that my bf could basically carry us through the whole thing. It wasn't until the end when I finally got a grip on things that I was actually of any use lmao.
Resistance: Fall of Man. The first one, we still haven't beaten due to circumstances, but honestly, we've been itching to play for a while. To us, it's a great hilarious co-op experience as we've been trying to go through it, especially with me so new to shooters.
Dynasty Warriors 7. Okay, no clue how this is in two player mode, but I've enjoyed it, there's enough customization that it soothes my RPG itch (which is a huge itch to me) and still has a general beat 'em up. Although it's completely superficial, it's also nice to see those KO counts sky rocket, and for a newbie, even a girl, it's a pretty good feeling :x.
Assassin's Creed. This one is a bit of a stretch, especially since it's single player, but honestly, I've enjoyed watching my bf play it, I thoroughly loved the story line. Now, it does get a tad repetitive, so like I said, it's a stretch, but it can also introduce her to other types of games.
DA:O. Play together, create a character and allow her to help design him/her and role play. Make sure one of you is decisive though. This is how my bf introduced me to DA:O and we hardly got anywhere because he didn't want to mess up "my character" but I didn't want to screw up "his character" lol.
Either way, try picking a game you both will enjoy, and remember to stay open. If she's not feeling a game, don't try to force her to continue, ask her for her input and ask her for her opinions. It's the companionship that makes co-op awesome, especially for couples. Have fun
