Nomadic Fanatic said:
If you don't mind trying out the older original Xbox titles that are 360 backwards compatible:
Burnout 3 - it's not really a driving game. It's an adrenaline rush that tests your memory and reflexes. Fastest. Game. Ever.
Sid Meier's Pirates!
The Simpsons Hit & Run It's better than The Simpsons Game for PS3/360 even though it came out 4 years earlier. Go figure.
Far Cry Instincts Seriously, I don't know why I love this one. It's...different from the other FC games. They made a 360 version of it as well, called Far Cry Instincts Predator.
Ghost Recon The first and best. Ever want to control ALL of your team members? Yeah, this is one of the few that allowed you to do that. Your team member AI can get stupid sometimes though.
GTA San Andreas Eh, just get it on Steam.
Splinter Cell - I recommend the first one just to see where it all began but really the first three are great.
Black - A "test" game by Criterion, makers of Burnout. FPS with a lot of destructive environments and enemies that can take 20 direct hits for some reason.
And if you have an NTSC (US and Canada) PS2, I recommend Shadow of the Colossus. If you already have it, get the component cables for PS2 and play the game at 480p, widescreen. Gran Turismo 4 could output 1080i (NTSC only), but I wouldn't recommend the GT series if you're not into cars. Hell, there's a ton of PS2 games that could do 480p [http://en.wikipedia.org/wiki/List_of_PlayStation_2_games_with_HD_support] so if you don't have the component cables I recommend getting them.
If you like in the UK or Europe, I recommend
Vib Ribbon, a PS1 game. It was never released in the US, but I have a chipped PS1 and a Japanese copy. It's...I should let the video do the talking:
Also, check out
Oni for PS2. It's basically a Ghost in the Shell videogame, only it was made by Bungie. The controls can get weird though because your rotation also controls pitch, so you might find yourself fighting some guy and then suddenly staring at the ceiling. It's got a great system where you can transition from hand-to-hand to guns.