A few games that others have mentioned:
Gears of War 1--it comes packed with Gears of War 2 and a bunch of bonus maps, now. I think the asking price is pretty cheap, now. You may have already played it on the PC and you can probably find GeoW2 cheaper as a stand-alone, but there's really no good reason to buy GeoW2 individually when you can pretty much get the DLC and GeoW1 for free, now.
Magna Carta 2-Is a great jrpg but I can recognize that it isn't for everyone. I got it for Christmas in 2009 and I couldn't even play Mass Effect 2 until the game was done. The story was a bit cliche and the dialog presentation was a little off-putting but I found myself simply addicted to the gameplay. Like I said, not for everyone but once you learn the battle system, it's like crack. Try before you buy.
Bully- An all around great effort from Rockstar and worth owning if you don't have the Wii/PS2 versions. The graphics are shit but the game is very enjoyable. It's supposed to have a couple of exclusive classes and such but I doubt you'd even miss them if you played one of the other versions.
Infininte Undiscovery--Started out great but after about the halfway point, descended into monotony. I can't recommend this game in good faith. It needed a lot of polish in the gameplay/graphics department and there was one part where I was stuck with a dead game, due to a poorly placed save-point. I'd say skip it in favor of Magna Carta 2, Lost Odyssey, or Blue Dragon (I own it but haven't given it enough time to fall in love with it, yet).
Ninja Blade--A great game with great presentation, really tight feeling gameplay, and a heavy reliance on QTE's. The QTE's are pretty forgiving but are very abundant. If you can tolerate them, this game will be worth the money. It does have some truly awesome "HOLY SHIT" moments that will make you smile. The story is poorly written and embarrassing, though. Still, I recommend it purely as a throwback to games like Ninja Gaiden (nes) where nobody thought it was unusual for a ninja and a giant spider to fight.
Some games that I own but don't think are must plays include: Bulletwitch (not polished enough to be a contender), Burnout Revenge (available on last gen consoles but really must be experienced on 360--my favorite Burnout, even today), Saints Row (nowhere near as good as the awesome sequel), Commanders Attack (a ripoff of Advance Wars for XBLA), and Kameo (a game that I LOVED in 2007 but probably isn't so good, now). I say try these games if they're dirt cheap. You'll get some fun out of them if you ever end up really bored and in need of something to distract you. They just aren't AAA status, though. None of the games in this post are.
