6. Grand Theft Auto IV (Xbox 360)
*Disclaimer! I haven't played GTA V yet, so I'm just talking about the series up to GTA IV.
This is probably the 360 game I've played the most and can still play constantly. I've always liked the GTA series, but they definitely outdid themselves with this one. I really love the attention to detail in this game, such as pedestrians walking around with cigarettes and coffee and checking cell phones. The protagonist, Niko Bellic, is my favorite in the series and I love the whole "an immigrant trying to make it in America" plot. LCHC is such an awesome radio station too and gets even better in the Lost and the Damned DLC with the addition of extreme metal. I can entertaining myself for hours on end doing pointless shit in this game from mass killings to dicking around in a helicopter to just browsing the "internet," laughing at Rockstar's spot-on satire.
Other great games in the series: Grand Theft Auto III, Grand Theft Auto: Vice City