Looks like the first game for the Xbox 360 that has usable cheat codes (that also allow for the unlock of achievements) is Tom Clancy's Ghost Recon Advanced Warfighter.
Here are the CONFIRMED cheat codes:
Gameplay cheats
Press start during the game and while on the pause menu hold the back button, Left Trigger, and Right trigger and enter the password
Y, RB, Y, RB, X = (Input on the Mission Select Screen) All Levels
Y, Y, X, RB, X, LB = Scott Mitchell Invincible
X, X, Y, RB, Y, LB = Team Invincible
RB, RB, LB, X, LB, Y = Unlimited Ammo
LB, LB, RB, X, RB, Y = Put your life at 100%
Of note, you have to Press (and then hold down) the buttons IN SEQUENCE (Back, LT and RT) before you can enter the codes. You will also hear an audible noise when the code is accepted.
You also need to re-enter any code after each level is completed.
Z
Here are the CONFIRMED cheat codes:
Gameplay cheats
Press start during the game and while on the pause menu hold the back button, Left Trigger, and Right trigger and enter the password
Y, RB, Y, RB, X = (Input on the Mission Select Screen) All Levels
Y, Y, X, RB, X, LB = Scott Mitchell Invincible
X, X, Y, RB, Y, LB = Team Invincible
RB, RB, LB, X, LB, Y = Unlimited Ammo
LB, LB, RB, X, RB, Y = Put your life at 100%
Of note, you have to Press (and then hold down) the buttons IN SEQUENCE (Back, LT and RT) before you can enter the codes. You will also hear an audible noise when the code is accepted.
You also need to re-enter any code after each level is completed.
Z
