Here is my list of games she may enjoy.

LittleBIGPlanet
PixelJunk Monsters
Uncharted
Buzz: Quiz TV

Although this may not work I found it to be flawless in my attempt to get my girlfriend into some more serious gaming, plus it is cheap.

Final Fantasy IX

My girlfriend couldn't but get enough of the Zidane/Dagger love story there. She even got upset during the ending, I made her think Zidane died.

She may even like Disgaea for the humor. My girlfriend was iffy about that game, she said she didn't care for strategy games. I opened up Youtube, turned on a couple of Disgaea episodes, she found it to be funny as hell and she instantly fell in love with the characters.

She then breezed through Disgaea 1, Disgaea 2 and then Disgaea 3, all within a matter of 1-month.

PixelJunk Monsters (you can play co-op) and LittleBigPlanet

Hmm, if she likes old Tomb Raider, then you could try her with a Prince of Persia. But that'd probably be a rent first thing, unless you like PoP that is

As for mario, Galaxy is always good 2 player co-op

As for things that the stereotypical female gamer might enjoy

LBP, Kororinpa, Boom Blox, Wii Fit could all work (maybe wait for kororinpa sequel, I hear it is good)

I would get Killzone 2. If she doesn't like it. Dump her :p

ratchet and clank future

I got my girlfriend Final Fantasy IX for christmas. But, Uh, I dunno.

Um, just buy Mario Galaxay. It's an amazing game and she'll love it. Guaranteed.

New Super Mario Bros. and the Pheonix Wright games for DS. Every dame I have seen play it, loves it.

     That's hilarious to me, because that's the exact same gateway drug I stumbled upon to get my girlfriend into RPGs. Maybe there's something about FF IX?  It has an incredibly charming beginning, that's for sure.  Haven't yet gotten her to play strategy games, but she has beaten most of the Final Fantasies, Suikoden V and most of II, Fable II, and Tales of Vesperia.  My next move is Chrono Trigger.

       I would recommend LBP if you want to

1.) Play the most hilarious and fun co-op experience I've played in over a decade (ever?) - it also works really well, allowing you to combine online friends with local ones.

2.) try a creative game you might get hooked on similar to an MMO (but with less of the feeling of sucking hours of your life away for imaginary loot and prestige, and more emphasis on exploration and enjoyment).

My wife enjoys Psychonauts for PS2, as well as Indigo Prophecy. For Wii, she loves Mario Kart Wii, Trauma Center, and Warioware Smooth Moves. And for 360, she loves Bioshock (and they make that on PS3 now, so it may be an option for her). Hope this helps!

LBP, Uncharted and Flower, Those three are great. And you cant go wrong with Super Mario Galaxy and Mario Kart