You're a little late. You grabbed a system that many people felt was technically behind the curve when it launched, five years after it launched! But fear not. It's home to some truly great experiences, if you don't mind the 'less than state of the art' graphics. Some games appeal to people who've grown up with Nintendo franchises more than others. With that said:
- Donkey Kong Country Returns and New Super Mario Bros. For some of the best 2D platforming you will ever find.
- Metroid Prime Trilogy if you have an itchy trigger finger and want some of the best adventuring on the market (MP3--included--was my pic for best game of the generation for quite a while)
- Metroid: Other M is a unique and fun game. Don't listen to the haters!
- Silent Hill: Shattered Memories for some mature rated, scary fun.
- Super Mario Galaxy 1 & 2 for the best 3D platforming the world has ever seen (I like SMG1 a bit more, myself)
- Punch Out!! for some old schol, arcade style fighting
- Wario Ware: Smooth Moves to see what a Wii Remote can really do (I can't describe it but it's too much fun!)
- Mario Kart Wii for a Kart Racing game that never gets old.
Anyway, these should get you started. If you're looking for some FPS, TPS, or certain other experiences like that, I'm afraid you may have to look elsewhere for the best on the market. But there's a ton of fun to be had with the Wii if you know where to look for it.