The most important thing, I think, is that the game must be immediately rewarding.
No lengthy cutscenes like Okami, no aimless sandbox-y wandering like Shadow of the Colossus, just something that throws her right into the action, preferably with a tutorial that gets more or less invisibly worked in the first few minutes.
Show her what the controls are once and give her the controller. Don't ask for it back, don't take it away, let her fuck up and make mistakes. If she likes the game she will want to learn from them, if she doesn't, that's an indicator she's not really into it and maybe you should try something else.
Regarding what kinds of games work... that depends more on the person than anything else. My girlfriend played through two Prince of Persia games because she liked the characters and the combat was simple enough to learn but flashy enough to make her enjoy it and feel empowered. Same goes with the controls - easy and intuitive to master, with flashy, colorful results. Hence what I was saying earlier - the game must be easy to master and immediately rewarding. Telling her the game gets better halfway through isn't much of an incentive when you're new to this.
Co-op games are good too. My girlfriend is a big fan of the early SNES Kirby games. As the helper, she can fuck up as many times as she wants, because as Kirby I can revive her just as many times. So there's no pressure on my side, and she gets to do whatever she feels like doing, and all the way feel part of the game, sans penalty. I think simple puzzle platformers are a good pick, and co-op makes it more fun.
Lastly, any game with a good story or characters may catch her eye (as in, if they're interesting to her tastes). Now that really depends on what she likes and what she doesn't. The important thing is 1) don't force anything on her, 2) let her learn from her mistakes and 3) offer assitance or hints rather than taking over.
