Sorry, I wanted to answer after work yesterday and then my internet died...
I have to admit, I'm not the best person to ask about other games, and one of my friends who is a gamer prefers his XBox over the Wii. But what I've heard is that the Wii is good for party games. I enjoy Mario Kart, Wii Fit is surprisingly fun despite not being a great way to be "fit" (requires a balance board, though), and Super Mario Galaxy and its sequel are supposed to be great. You can also get things like Rock Band for the Wii. Then, of course, there are all those "old school" games on the virtual console. Not gonna like, the virtual console was my secondary reason for getting the Wii.
If you plan to get the accessories to play Gamecube games on the Wii, some of the recs threads should have recommendations for those - there are supposed to be some really good ones out there and they're 25 - 50% of the prices of new Wii games. One of the ones I have and still need to play is Paper Mario and the Thousand Year Door. If you like fighting games, Soul Caliber II is good. The Animal Crossing series (the original is on the gamecube but there is also a new release for the wii) is also really popular if you're into life sims at all.
In the end it comes down to what kind of games you like and how much you plan to play the Wii, though.