Master cheat:
At the Main Menu, select 'Extras' and 'Cheats'. Now enter YZWZYXWX or WWXXYZYZ to unlock all in-game cheats. During play, press Esc to access the cheat menu, then just activate whichever ones you want.

Individual cheats:
Alternately, you can enter one of the following codes at the 'Cheats' menu to unlock specific codes:

Y             All weapons
X             Explosive personality (press 'Use' to kill)
ZYXWYZXX      Level select (at single-player menu)
YWXZYZXW      Infinite ammo 
ZYZYXXWW      Rapid rails
YYYYYYYY      Rain of fire
XXXXXXXX      Walking dead 
WWWWWWWW      Wacky deaths 
XXYWYWZ       Super health 
XXXXYZXX      Gibby ammo
WZXYWZXY      Gibby explosions 
ZXZYXZXZ      Unlimited grenades 
YXZWZXYW      Director's cut

Thanks to Revolution readers DOC_1069, DLIGHT102 and James Brody!