You want a great storyline? Pick up Bioshock 1 and 2. Both are relatively short games, but the story is amazingly immersive. You absolutely don't want to put it down.
Another story game, Red Dead Redemption. I was on a leave of absence for a hernia from work for 2 weeks and put 40+ hours into that game. Absolutely brilliant piece of work.
Other games that every 360 owner should have are Gears of War and Gears of War 2. I'm so pumped for Gears 3 it's not even funny. I spent so much time playing Gears 1, the online was so amazing. They totally screwed up Gears 2 with matchmaking and I hope Gears 3 goes back to its roots.
And everyone wanting a racer, skip Forza, skip Grid, Dirt, etc..... TWO WORDS.... Hot Pursuit. Criterion games now has a chance at the Need for Speed franchise and is releasing Need for Speed Hot Pursuit AGAIN!!! I'm so reaking pumped, Hot Pursuit 2 sucked hours out of my life on ps2 and i hope that the arcade racer genre gets some life back into its lungs this november. Watch the trailer here
Need for Speed Hot Pursuit