I'm going to try to limit my recommendations to what I think are the essentials:
1. Wii Play
2. Wii Sports Resort (releases late July)
3. Mario Kart Wii
4. Metroid Prime Trilogy
5. The Legend of Zelda: Twilight Princess
6. Punch-Out!!
7. The Conduit (releases next week in NA)
8. World of Goo (WiiWare)
I'd say those games are the essentials for Wii, I had never played Punch-Out!! before but it's a very very well put together game that really gives a challenge and does give you an old school type vibe. It's awesome.
I'd also recommend the following in no particular order:
- Grand Slam Tennis
- Tiger Woods PGA Tour 10
- Super Smash Bros. Brawl
- Resident Evil 4: Wii Edition (If you haven't played RE4 before it's an essential)
- MadWorld
- House of the Dead: Overkill
- Super Paper Mario
- Mario Strikers Charged
- Call of Duty: World at War
Soon to be released recommendations:
- New Super Mario Bros. Wii
- Wii Fit Plus
- Red Steel 2
- Rabbids Go Home
- Dead Space: Extraction
- Mario and Sonic at the Winter Olympics
Next year:
- No More Heroes 2: Desperate Struggle
- Super Mario Galaxy 2
- Metroid: Other M
There.. Plenty of titles to choose from :)