The Witcher 2: Assassins of Kings -- My favorite game of 2011, though the Xbox version just came out a few months ago and is still pricey. (I saw it on sale for $30 recently; maybe you can find a deal.)
Now, the first game is PC-only, and in fact the whole thing is based on a series of Polish fantasy novels that were only recently published in English. But you don't really need to know all that stuff. Here are the important bits of the backstory:
It's a medieval fantasy setting, of the dystopian sort that's currently vogue. Think Game of Thrones, only even more bleak.
Witchers are mutants who fight monsters. They're all male, they have yellow eyes, age slowly, are immune to disease, can cast a few simple spells, and use various potions to enhance their senses.
Our Hero, Geralt of Rivia, is supposed to be dead, but for some reason he's not. He's got amnesia (and if you're playing an RPG cliché drinking game, drink up) and has recently been caught in the middle of a race war in the city of Vizima. A terrorist organization of elves and dwarves called the Scoia'tel invaded, a Knights Templar-like religious organization called the Order of the Flaming Rose seized control of the city, and ultimately the King of Vizima showed up and managed to regain control. The first game ends with Geralt foiling an assassination attempt on the King, only to discover that the would-be assassin has yellow eyes.
The PC version originally had a steep-ass learning curve (as Penny Arcade put it, "It's not that hard. You just have to use abilities they won't discuss and techniques they haven't entirely taught you via controls they never quite explain.") but I hear the Xbox version fixes that and has a tutorial section that doesn't just throw you in the deep end.
Sonic Generations: The first good Sonic game in a decade. There's a plot involving time travel that causes 2011 Sonic to team up with 1991 Sonic; you play through new versions of levels from previous games (Green Hill from Sonic 1, Chemical Plant from Sonic 2, etc.), and each is split into one 2D level you play as '91 Sonic and one 3D level you play as '11 Sonic. The conceit works really wonderfully; the levels are well-designed, full of nostalgia, and have some good remixes of the old music; there's not much to the plot but it's pretty funny (particularly when 1991 Robotnik meets his future self).
Sonic CD: And speaking of 1990's-vintage Sonic games, they've ported this one to the Xbox as a downloadable title. (BTW, a friend of mine advised me never to buy Microsoft Points directly from Microsoft; they store your credit card online, tie it to a Windows Live/Hotmail/Whatever account, and if one of their affiliate sites gets broken into there goes your credit card information. You're better off buying a Microsoft Points card at GameStop or wherever and then entering it into your Xbox.) A few tweaks here: the game works in 16:9, they've changed the spin-dash to work the way it does in Sonic 2 instead of the original clunky version, you can choose either the Japanese or American version of the soundtrack, and after you beat the game you can replay as Tails.
(I think they've got a bunch of other old Genesis Sonic games for download, but they haven't been updated in any way.)