I'm looking for a game for me and my girlfriend to play together online. The catch is that shes pretty new to gaming, so anything too complicated or twitchy might not work. Also, I don't want anything too violent or bloody, just a nice game for us to play together when we have some free time. Any ideas?

Have you spoken to her about what sort of game she'd like to try? Is she competitive, or likely to throw her hands up and quit when she feels like she has no idea what she's doing? (I know a lot of people like that, both male and female)
Online shooters, well.. You rarely get to play one on one, so maybe scrap that.
Guild Wars would be good purely because once you leave a town, you're in your own private questing area. So you team up with her, get some AI henchies/heroes and away you go.
Civilization 4 might be a bit full on.. Actually, try and find something with co-op.. Depending on her personality, there might be the slight possibility she'll become livid if you beat her.
Diablo 2 would be good for co-op, make a password protected game, get her to join and awesome times ahead. I used to play Diablo 1 with an ex girlfriend way back when it was released. We spent an unhealthy amount of time on that game.

Ah, girls who played Max Payne ^^".
Makes me consider starting a thread called "Looking for a gf for my game"...

HoMM 5 is basically 3 with quite a few neat ideas to improve on gameplay. You just need to find some custom maps to get the perfect gameplay out of it - not an issue, really.
I say it's girl friendly, 'cause it's graphics are just nice - and as much as it may be hard for us guys to understand, they usually have way more developed feeling for aesthetics than we will ever have :D Once you have her hooked up on 5, transition to 3 will probly be way easier.
And also, turn-based gameplay just doesn't force her to do anything fast, it doesn't rely on reflexes, nor does it rely too much on strategic thinking while battling against random encounters, so it's just pure fun - perfect game for a start :D
Oh, also good point with co-op play - 5 sadly does not include that, so it might be an issue. I do, however, remember times when I used to play 3 with my nephew quite vividly, and it was the original one, so no co-op either. And yet, it was very playable when we agreed to play together :D
Oh, when I'm reading trough the thread: Do not, under any circumstances, start playing D2 with her until she gets the hang of whole level-ups, equipment and skills thing, or you will NEVER get her to play it again - really, thing about how does the game look to anyone who only sees running around and clicking on monsters :D
And Civ4 might be fun, the whole aging throughout the history process is awesome, it might just be a bit too abstract thou. It's well worth the try thou :-) The only way I get my girl to play it with me is watching over my shoulder, telling me which religion should I make US to believe, and asking who the hell is that black guy.

casual games ?
http://www.orchidgames.com/heartwild_solitaire_book_two

Any of the older Worms games.
Worms, Worms 2, Worms Armageddon, Worms World Party ...
I've played some of these with several girls / women and they liked the games.

If getting her a 360 isn't out of the question, something like Uno might be a good idea

Oh right, worms, those can't be bad even if they wanted to.