I've no idea what games you've played but since you don't like shooters, have you tried:
The Orange Box (shooter but Portal is a fantastic puzzle game)
Forza Motorsport 2
Project Gotham Racing 3
Puzzle Quest: Challenge of the Warlords (XBLA)
Geometry Wars: Retro Evolved (XBLA)
skate
Project Gotham Racing 4
Dead Rising
Viva Pinata
Bomberman Live (XBLA)
DiRT: Colin McRae Off-Road
Crackdown
Pac-Man Championship Edition (XBLA)
Super Puzzle Fighter II Turbo HD Remix (XBLA)
Ace Combat 6: Fires of Liberation
Test Drive Unlimited
Marvel: Ultimate Alliance
Prince of Persia Classic (XBLA)
Command & Conquer 3 Tiberium Wars
Condemned: Criminal Origins
Saints Row
LEGO Star Wars II: The Original Trilogy
Uno (XBLA)
Rockstar Games presents Table Tennis
Catan (XBLA)
Cloning Clyde (XBLA)
Tomb Raider: Legend
Kameo: Elements of Power
Alien Hominid HD (XBLA)
Lord of the Rings: The Battle for Middle-earth II, The
Eternal Sonata
Marble Blast Ultra (XBLA)
Carcassonne (XBLA)
Blue Dragon
Every Extend Extra Extreme (XBLA)
Worms (XBLA)
XBLA = Xbox Live Arcade Game
Also coming up - Virtua Fighter 5, Mass Effect, Assassin's Creed, Naruto: Rise of a Ninja, Viva Pinata: Party Animals, Lego Star Wars: The Complete Saga, Scene-IT (party game), Resident Evil 5, Too Human, Alan Wake, Lost Odyssey, Devil May Cry 4, World in Conflict.