I have one. I like the rail-gun shooters on it, the Resident Evil Chronicles series. nice challenge, fun with a 2nd person, and zombies!
I also love RPGs on there, so I suggest picking up some Zelda games (for the gamecube ones you'll need a gamecube controller which are cheap to get), maybe get Tales of Symphonia (the first one) as it has a lovely storyline. Mario Kart is great for some fun racing, Soul Caliber for fighting as well as Super Smash Brothers Brawl (which you can play people over Wifi), and if you want scary, pick up Silent Hill Shattered Memories.
Best thing about a Wii is you can play Gamecube games, too, so don't hesitate to go back and look at those as well. (But you need the controller and I think a memory card, both are dirty cheap.)
I love my Wii and my PS3.