Street Fighter IV maybe? Civilization Revolutions? Carcassonne? Dungeon Defenders maybe I don't p lay MP so that's all I got. Oh, but I definitely second Words With Friends (depending on her English skillz)
Words with Friends All the rage at my school and has asynchronous online MP with a chat window. I assume your GF spends her time singing 'Moskau' and 'Katyusha', and drinking vodka of course, this could be the game for her.
About the best recommendation I have for a co-op game you both could play that is actually quite fun and works well co-op is "Lara Croft and the Guardian of Light". Even has female and male characters... Warning though - I've only ever played it over wifi but I know you can play it over Gamecenter although I have no idea how well it works over Gamecenter. I play it just fine with my son over local wifi - I have an iphone4 and my son has an ipod touch 2nd gen. Star Battalion you can also play over wifi through Gamecenter and its co-op but not as much fun as Lara Croft is (but I also haven't played it over Gamecenter). Dungeon Hunter 2 can also be played co-op online through Gameloft's servers or through Gamecenter (but, once again, I haven't tried it over Gamecenter). That could be very fun - especially if you're into RPGs. EDIT: Wanted to point out that I'm not really recommending Star Battalion - I was honestly not impressed with the co-op experience but it might just be me.
Nice post. DH2 and LC definitely have impressive coop experiences. By tonight, we can add Rainbow Six to this list. You're right about Star Battalion; the online play is very limited and boring.
