I enjoy playing my 360 a lot. I also like going back to my regular Xbox and playing some classics on that
I enjoy Jade Empire, KOTOR or Fable when I want to sit down and be entertained by both gameplay and storyline. I play Black, Castlevania: Curse of Darkness, or Crimson Skies if I want to listen to music/talk radio or just screwing around, not really having to pay attention to what I'm doing in the game.
My 360 I like playing GTA IV, Dead Rising (I love that game!), Mass Effect, Command and Conquer 3 Tiberium Wars, and Bioshock I love to play when I show attention to my 360!