I'm only going to list the games I already own (leaving out Wii Sports and Play) because I can't judge the others:

1.The Legend of Zelda: Twilight Princess
2. Excite Truck
3. Wario Ware: Smooth Moves
4. Sonic and the Secret Rings
5. Rayman Raving Rabbits

No particular order. I put a few extra because I included soon to be released.

1. Zelda TP
2. RE 4 Wii Edition
3. Excite Truck
4. Madden 08
5. Metroid Prime 3
6. Super Paper Mario
7. Godfather BHEdition
8. Super Mario Galaxy
9. Easy 15 different VC games
10. Metroid Prime 1 & 2
11. Super Smash Bros Brawl
12. Sonic and the Secret Rings
13. Rayman Raving Rabbids

hope this helps.

Mario Strikers Charged is great multiplayer fun.

 You won't be disappointed in Eternal Darkness.  I really would like to see a sequel sometime here.

I'll assume you already have a gamecube and that's another list entirely:

1. Zelda TP
2. Excite Truck
3. Godfather Blackhand Edition (The Wii controls *make* this game)
4. Super Paper Mario
5. Resident Evil 4
6. Trauma Center: Second Opinion
7. Madden '07 (Don't let the PS3/360 versions trick you -- the Wii version is very good)
8. Wario Ware: Smooth Moves
9. SSX Blur (I love this game)
10. Rayman Raving Rabbids (if you have friends)

These are just games I own which I'd recommend. There are some other games which I own I'd recommend as well (Big Brain Academy, for example), but some people may or may not like them, so it may be worth borrowing or renting them first. I don't have Mario Strikers Charged yet, which looks like it may be awesome, and I also don't own Elebits which many people praise. So don't consider this list inclusive of all of the great Wii games out there simply because there are a surprising number of very good games already available for the little white box.

There are only 4 Wii games every Wii owner should have and they are:

1. Zelda: Twilight Princess
2. Super Paper Mario
3. Mario Strikers Charged
4. Resident Evil 4 (if you never played the original)

Old Snake speaks the truth. These are the only games I'd pay the full price for, although there are a few others that are worth getting for under 30€ or borrowing from a friend.