My girlfriend plays a lot of games (and not just for attention). The games she plays by herself are: Cubivore, Dig-Dug, Donkey Kong, Kirby 64, Luigi's Mansion, Mario Pinball Land, Mr. Do!, Pac-Man (or Ms.), Shanghai Pocket (GBC), Snood (GBA), Super Mario 64 (DS), Tetris (any), WarioWare, and last but not least Yoshi's Island (her fav)
The games we play together (from time to time): Animal Crossing, Bust-A-Move (any), Donkey Konga, Final Fantasy:CC Gauntlet (any), Katamari Damacy, Leg of Zelda: 4 Swords, Light gun games (any PS1, PS2, or DC), Mario Kart (any), Mario Party (any), Mortal Kombat (any), Super Smash Bros (any), Trivial Pursuit Unhinged, Worms (Armageddon or 3-D)
Games we've beaten together: Baldur's Gate 2, Champions of Norrath, D&D Heroes, Lord of the Rings: Third Age
Also, for our third year anniversary, she suggested getting a Gamecube (on launch day). She would get Luigi's Mansion and I would get SW: Rouge Leader. She figured that's better than dinner, roses or a movie. She just said "dinner and a movie we can do anytime and roses die after a week or so, but the Gamecube we'll be having fun with for years." ......and who am I to disagree?