Seeing as how my girlfriend is a non-gamer, I figured out precisely what games she finds attractive. First of all, Wind Waker- she really loved the world, the pacing and the combat. Being Japanese she remembered games like Dragon Quest and FF. After playing Wind Waker she couldn't figure out why people still play turn-based RPGs. She loved Tetra, because she's a strong central character, and she loved Link because he is simple and cute.
The next game, or series rather, that she holds so high above all else is Pikmin. This game just blew her mind. She couldn't wait to pick up her copy Pikmin 2 when it first launched in Japan. She got the soundtrack, the toys, the plush. Needless to say, she loves the game for its intuitive design and cute characters.
Thirdly, and most common among all of us with hos, is Animal Crossing. The idea that you CAN'T die and that there is no timer made this game extremely appealing to her. The world let her exlpore it at her own pace, and at the same time send letters and things to me.
Other games she really enjoyed and played to the end were Wario World*- extremely well balanced controls and level design. Very fun and easy-to-understand gameplay makes it very appealing for non-gamers. Kuru Kururin- One of the Cube's best in my opinion. She also played this to the very end. Something of a rarity. She loved Mario Party 4 & 5, as well as Mario Golf, because you can take your time and plan your strategy. Remember girls like games that have a lot of strategy and planning, but are also very intuitive. If you think about it, the games girls like are probably the best designed. Guys can sacrifice a lot just because they like the game's theme (GTA, HALO).
*Seriously, give her Wario World. She will love it. I think a lot of people crap on the game's difficulty, or lack thereof, but it is hands down one of the most satisfying platformers out. Trust me, there's no BS'ing girls with gimmicky themes. They just want the best gameplay, the best design and the best controls.