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?

Hmm, you can go with Sleep is Death and make her some nice stories to play through if the graphics aren't important.
Another option would be Guild Wars as it doesn't have a monthly charge and the instances are restricted to your group which means that it'd be just the two of you.
You can even try Team Fortress 2 because the graphics are cartoony and she might not mind them and the pace is slower than in other shooters (and she can also play medic and just follow people around and heal or engineer and build stuff and stay next to it).
Unfortunately there aren't that many options for (online) multiplayer that don't involve violent and bloody or complicated :(
Now, if it was a single player game I would of had more options.

Hmmm...Altitude? There's a demo you can try, too...

Well, if you just want to break her in on online gaming, you could always try something like FreeRealms. It's meant for ages 10 and up so the learning curve is pretty gentle, if you can handle the tweens hanging around (I checked it out to see if my oldest would be interested). You can ignore basically everyone except each other though. It's free, so no breaking the bank just to try it.

I know alot of people hate it for various reasons but World of Warcraft I've always found is pretty good for getting new gamers into games. Also playing it with people you know makes it much more fun.

Portal 2 is supposed to have a co-op mode. Which might make it an ideal choice when it's released. Worth keeping an eye on at least.

I highly recommend Sleep is Death too.
Also, Darkwind. I know players who've introduced their non-gamer wives/gfs to this game.

World of Goo!
Nice food + sweet drinks + lovely music + World of Goo = wonderful night!
(or the same with Peggle Nights)
(from experience :p)

Heroes of Might and Magic. I play those all the time with my girl ever since we got together - and she wasn't too much of a gamer either at first - well, it was the first strategy she has ever played. We're together for two years, for the record :D
It has nice graphics, especially fifth one is girl friendly.
Oh, and sleep is death is a fantastic idea as well.

Whatever you do, don't give her the Sims or you can kiss your computer goodbye.

By "online", do you specifically mean MMOs?
If you want to get her interested in MMOs, may I recommend Puzzle Pirates? It's cute, doesn't require a great deal of commitment, has a lot of variety, the minigames are nice, and you can try it for free. For something a little more in the vein of traditional MMOs, Guild Wars wouldn't be bad either.
For more general multiplayer, you could try a racing game. When I used to LAN a lot, we discovered that the girls would usually prefer playing Need for Speed: Hot Pursuit or Twisted Metal Black over FPS or RTS games.
For casual offline gaming, I've spent several hours with my wife just chilling out and playing Popcap/Spintop games. Even their search-and-find style games (Escape from X, The Wizard's Pen) are good fun.

Not sure if The Nations Gold Edition, or Settlers II Gold, or the Settlers Heritage of Kings may fit the bill of what you are looking for in a game.
They are fun, not too much violence and may have the features you are looking for to play with your GF.

Halo would probably be a pretty good game to start with. Its easy to learn and not to violent so even non gamers can have fun with it.

I vote for crazy/funny indie games, with some nice music. That's for a start, then you can evolve to a simple MMO or simple RTS.
Like El_Caz said, don't give The Sims to her, also don't give WoW. Or your girl will end up leaving you for the game. :p

Ha! Words of wisdom!