The 360 experience IMO is all about the multiplayer -- you're really missing out.
However, a short list for you.
Assassin's Creed
Mass Effect, though an RPG, features real-time combat that you may enjoy.
Bioshock
Prince of Persia
Ninja Gaiden II (the first is downloadable via Marketplace, and is even better)
Bionic Commando: Rearmed
Braid
And that's it for solo games. If you decide to get a Gold subscription:
Street Fighter II HDR
'' '' IV
Soul Calibur IV
Bionic Commando (lengthy single-player campaign also)
GripShift
Age of Booty
Bomberman Live
1vs100 (free trivia show for Gold members)
(any FPS games, but you may prefer them on PC anyway)