Zack and Wiki
Resident Evil 4: Wii Edition
Metroid Prime 3: Corruption
Zelda Twilight Princess
Super Mario Galaxy

Here's another vote for RE: Umbrella Chronicles and SSX Blur.

RE:UC has absolutely fantastic replay value about it, is great fun to boot and an excellent addition to the RE series, and any Wii collection.

SSX is just one bloody hard game, but very rewarding and satisfying to play, one of the first Wii games to shove a finger up to the morons who said the Wii couldn't do 'hardcore' games! ;)

List:

Zelda Twilight Princess - MUST
Super Mario Galaxy - MUST
Super Smash Brothers Brawl - MUST
Resident Evil 4 - MUST (Even if you played it before)
Metroid Prime 3: Corruption - MUST

Others:

Zack a Wiki - Great and Fun
Wii Play - for the extra Wiimote
Super Mario Paper
Resident Evil - UC
No More Heroes
Guitar Hero III

Game Cube games you might want to try:

Zelda The Wind Waker - MUST
Metroid Prime - MUST
Mario Sunshine - Didn't like it but it's Mario anyway...

Wait till Mario Kart Wii.....Gonna be an awesome game.....LoZTP and MP3 are great BTW

Mario Kart is the reason I decided to take the bus to the mall every day until I got myself a wii....can't wait for that game.

Basically, everything that I have down in my sig.

Brawl is a must own, if you have to ask why, then you shouldn't own a Wii. Actually no, I'd just doubt that you've ever been online before, but still, just look around, you'll figure it out.

Excite truck is great for simply driving around and having fun, with how the tracks are laid out, it's almost like being in a rollercoaster where you don't have any tracks and there are other coasters that are trying to beat you and will run you off the road to do it.

Twilight Princess and Metroid Prime 3 are excellent games, and basically demonstrate perfectly why the Wiimote is the best controller ever. However both only took me a single rental period to beat.

No More Heroes is the only mature game I've ever been interested in. It's blood and gore galore, but it's much like Kill Bill in that the amount and ways the gore is implemented becomes downright farcical.

I'd also recommend Fire Emblem: Radiant Dawn