If you're going for a Wii, the best multiplayer games are (barring Wii Sports, which comes packaged):
Mario Kart Wii (racing)
New Super Mario Bros. Wii (multiplayer platformer)
Super Smash Bros. Brawl (fighter)
These three are the triumvirate. Easily the most addictive and satisfying multiplayer on Wii, and single player is good, too.
Other Multiplayer:
WarioWare: Smooth Moves (very wacky)
Wii Sports Resort (don't have it, heard it's good)
Wii Play (decent if you get bored of Wii Sports)
For rewarding single-player experiences:
Super Mario Galaxy (platformer)
Super Mario Galaxy 2 (ditto)
The Legend of Zelda: Twilight Princess (adventure/puzzle)
Metroid Prime Trilogy (first person shooter/adventure)
Donkey Kong Country Returns (platformer)
Okami (adventure/puzzle)
Fire Emblem: Radiant Dawn (strategy rpg)
The top four of these, though single player, do tend to be gf-friendly. Engaging experience, fun without frustrating, etc.
Hope that helps. I have a Wii and a ton of games for it, though I tend to know more about what's good for single-player rather than for parties and such. Still, can't go wrong with the top three.
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