Any specific genre you're interested in? There are a whole ton of awesome games for the Wii, so if you could narrow down what you're looking for a little bit, that would help.
Action/Adventure
If you haven't played it yet, get Zelda: Twilight Princess. Awesome game, very long, lots of stuff to do, decent story, good Zelda gameplay. You can't lose with this.
If you want something other than Zelda, check out Metroid Prime 3. I would say get the Prime Trilogy, which would have all 3 Metroid Prime games in it, but apparently there aren't too many of those around for purchase anymore. Anyways, Metroid Prime 3 is a lot like Zelda; emphasis on exploration, lots of cool equipment, and great gameplay.
2D Platformers
The Wii really shines here. If you're looking for a challenge, get Donkey Kong Country Returns. It's an amazing game, with lots of replay value, and really tough level design later on. If you want something a little easier, go with New Super Mario Bros. Wii. It still has a decent challenge, is pretty long, and has a bit of replay value. If you want something even easier, go with either Kirby's Epic Yarn (piece of cake difficulty), or Kirby's Return to Dreamland (haven't played it, but Kirby games are never terribly hard).
3D Platformers
No brainer here. Get Mario Galaxy 1 or 2. Honestly, it doesn't really matter which one you get; many people prefer one over the other, but they're both amazing games. They're both pretty easy to beat, but to complete 100%, they have a good bit of challenge. Beyond that, the gameplay is simply awesome, the graphics are really superb for the Wii, and the replay value is really good too.
Multiplayer focused
Smash Bros. Brawl and Mariokart Wii are the two that shine here. Chances are, if you have had your Wii for very long, you have both of these already. However, if you don't, I highly recommend both of them. While they are definitely multiplayer focused, you can still have a bit of fun with them alone, and if you have no-one to play with, I'm sure people still go online with them.
Those are most of the main big ones.