Xbox 360

BioShock
RDR
Dark Souls
Fallout 3
Mass Effect 1-3
MGS4
MGS: Peacewalker
Rock Band
Modern Warfare 1
Half Life 2
Arkham Asylum and Arkham City
Portal
Mother 3 (came out after the 360 did so I will still count this)

I'm sure they're more but those were the first that I thought of.
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GT: TheAnalogKid06

Skyrim
Red Dead Redemption
Far Cry 3
The Walking Dead
Heavy Rain
Enslaved: Odyssey to the West
and, even though it was a PC game done in a 16-bit graphical style, To The Moon!
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Currently playing: Lots of N64, PlayStation, PlayStation 2 and Dreamcast

Twilight Princess
Project Gotham Racing 3 (first time I saw 360/PS3-level visuals)
the final twists in Phoenix Wright: Ace Attorney
Rock Band series
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www.backloggery.com/gamerjm http://i.imgur.com/G4xvV.gif
"they should lock you up and throw away the key"-jobb_UC on me

Just Cause 2
Red Dead Redemption
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Red Dead Redemption - Not a fan of westerns but this game made me appreciate what people like about em. Marston was an awesome character, I wish they would have allowed us to see what he was like before he reformed into the person he was in the game.

Arkham Asylum / City - Batman being my favorite superhero, I felt these games did his persona justice, can't wait to see what the next Arkham adventure brings. Hoping it's like AC but with the feel of AA -- on a much larger scale, maybe vehicle use?

Fallout / Skyrim - Need I say more? These games are awesome and you can waste hundreds of hours doing .. absolutely nothing .. which is a good thing.

Halo 4 - 343 brought Chief back in awesome fashion, everything about the game is insanely fun - can't wait to see what the rest of the reclaimer series does on next generation consoles.

Forgot some PS3 games.

Heavy Rain - Awesome game, most people are not a fan of the QTE stuff but I found it made the game a lot more enjoyable, you kinda have the option of either succeeding or failing, changes the story the way you want with certain characters - can't wait for Beyond: Two Souls.

MGS4 - The reason I bought a PS3 to be honest .. love the series, MGS3 being my favorite but this game did what it does best .. tie up loose ends while opening new plot holes, cannot wait for Ground Zeroes.
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XBL - FA7ALtheGOD / PSN - FATALtheGOD
Who dares, wins.