I heartily recommend the Mass Effect series. A truly wonderful science fiction/rpg epic. Has a bit of a sand-box feel as you do have the freedom to explore rather then just stick to a story.
For pure all out fun Just Cause 2 is excellent, the story is just... stupid, but you are given an entire island nation to run around in and take liberties with.
Enslaved: Odyssey to the West is a puzzle/platform/action game with outstanding facial animation and story telling. It features motion capture performance by Andy Serkis and is an undiscovered gem.
On the XBox Live Arcade, take a look at Limbo and Braid, two 2D platformers with outstanding graphics and puzzle elements. Also, Trials HD is an update of the old 2D flash motorcycle trials games, it is horribly addictive.