Batman: Arkham Assylum and Arkham City 
 Burnout Paradise 
 Dragon Age series 
 Dark Souls + Demon's Souls 
 Battlefield 3 if you trust the hype. 
 Borderlands (A sequel is coming up if you want to wait for that) 
 Splinter Cell series 
 Ninja Gaiden 2 
 Grand Theft Auto 4 
 Assassin's Creed Series (If you care about the story, go it in order. Otherwise, start with the second game or wait for the third to come out soon) 
 Asura's Wrath (Suggested Rental than purchase) 
 Bioshock series (I prefer the first to the second, a new title releases this year) 
 Brutal Legend (Stars Jack Black, what's not to love?) 
 Bully (A Rockstar Title that got a judge to publically denounce Jack Thompson's opinion. Yay!) 
 Dead Rising Series (You'll prefer the story in 1 but the freedom in 2, DLC and Case West to avoid unless you care for story sake) 
 Fable Series (My favorite is 2, but the whole series is pretty linear despite the areas you can go) 
 Fallout Series + DLC (DLC adds story, play time and more. Start with Fallout 3 for story + simplicity or New Vegas if you want to focus where the first two games existed + all enemies free to fight from the beginning, even when one hit deaths occur) 
 Gears of War Series (I've heard that 1 is better than 2 but I've only played the second) 
 Halo Series 
 Hitman Series 
 LA Noire 
 Mass Effect Series (If you don't mind DLC for game 3's ending) 
 Overlord Series (Suggested Rental) 
 Prey (Suggested Rental, new title recently cancelled I believe) 
 Prototype (Suggested Rental, sequel currently released) 
 Saints Row Series 
 The Darkness Series 
 The Elder Scrolls Series 
 Bayonetta 
 X-Men Origins: Wolverine (Suggested Rental) 
 
 There's some decent titles on XBL as well, though I've only purchased and played Scott Pilgrim Vs The World. Most downloadable games offer a demo.