My favourite game on the Wii (and it ranks up there on my 'all time' list) is without a doubt Mario Galaxy. That game is simply amazing, it truly is an experience that you never want to end -- which makes sense for there to be a sequel coming out next year. The level design is so varied, it handles great and the graphics are brilliant for the system. Honestly, if you own a Wii and you don't have Mario Galaxy then you're missing out big time.
Other stuff you should check out, although obviously it all depends on what you're interested in, is:
- Mario Kart
- Brawl
- Paper Mario (what can I say? That guy is in good games)
- Zelda: Twilight Princess
- Zack & Wiki
- de Blob
That's just a selection though, there are many good titles out there that I don't own because they don't appeal to me, but they may very well tickle your taste buds. The Virtual Console and Wii Shop also offers some quality stuff (such as World of Goo and Strong Bad) on the download front.