These are the games I would recommend offhand. Some can be found on other platforms, and some are remakes from GameCube days... but they are all good games. You need to do some research though, because many of these games won't appeal to all audiences...
Animal Crossing
Boom Blox (& Bash Party)
Call of Duty: Modern Warfare Reflex
Dawn of Discovery
Dead Space Extraction
Disney Epic Mickey
Donkey Kong Returns
Endless Ocean (& Blue World)
Fire Emblem
Geometry Wars Galaxies
GoldenEye 007
House of the Dead Overkill
Kirby's Epic Yarn
Legend of Zelda: Twilight Princess
Little King's Story
MadWorld
Metroid Prime Trilogy
Monster Hunter Tri
Muramasa
NBA Jam
New Super Mario Bros
No More Heroes (& 2)
Okami
Pikmin New Play Controls
Pro Evolution Soccer
Punch-Out!!
Rabbids Go Home
Rayman Raving Rabbids (or TV Party if you own a balance board)
Red Steel 2
Resident Evil 4
Resident Evil Umbrella/Darkside Chronicles
Shaun White Snowboarding World Stage (if you own a balance board)
Silent Hill
Sin & Punishment 2
Super Mario Galaxy (1 & 2)
Tales of Symphonia: Dawn of a New World
Tatsunoku vs Capcom
Tiger Woods PGA Tour (10 or higher)
Trauma Center (Second Opinion, New Blood, or Trauma Team)
Wario Land Shake It!
Wii Fit Plus (maybe... you'll know if this is your thing or not)
Wii Sports Resort
Edit: Can't believe I left Zack & Wiki off the list. Really enjoyed that game, especially the puzzles in the second half. Also a big fan of the Sam & Max series... but recommend playing them on a different system if you have the option (for improved performance).