The cheats for both the PS2 version and PSP are the same, however, the multiplayer cheats don't do anything in the PS2 version.
Do not save after using these cheats because some can't be disabled!
Toni's Health
Get $250000
L1, R1, TRIANGLE, L1, R1, CIRCLE, L1, R1
Full Armor
L1, R1, CIRCLE, L1, R1, X, L1, R1
Full Health
L1, R1, X, L1, R1, SQUARE, L1, R1
Commit Suicide
L1, DOWN, LEFT, R1, X, CIRCLE, UP, TRIANGLE
Weapons
Weapon Set 1
UP, SQUARE, SQUARE, DOWN, LEFT, SQUARE, SQUARE, RIGHT
Weapon Set 2
UP, CIRCLE, CIRCLE, DOWN, LEFT, CIRCLE, CIRCLE, RIGHT
Weapon Set 3
UP, X, X, DOWN, LEFT, X, X, RIGHT
Police
Raise Wanted Level
L1, R1, SQUARE, L1, R1, TRIANGLE, L1, R1
Never Wanted
L1, L1, TRIANGLE, R1, R1, X, SQUARE, CIRCLE
Spawn Vehicle
Spawn Rhino
L1, L1, LEFT, L1, L1, RIGHT, TRIANGLE, CIRCLE
Spawn Trashmaster
TRIANGLE, CIRCLE, DOWN, TRIANGLE, CIRCLE, UP, L1, L1
Vehicles - Your Car
Improved Handling
L1, UP, LEFT, R1, TRIANGLE, CIRCLE, DOWN, X
Cars Drive On Water
CIRCLE, X, DOWN, CIRCLE, X, UP, L1, L1
Ride With Me
X, SQUARE, DOWN, X, SQUARE, UP, R1, R1
Change Bike Tires
CIRCLE, RIGHT, X, UP, RIGHT, X, L1, SQUARE
Vehicles - Traffic
Destroy All Cars
L1, L1, LEFT, L1, L1, RIGHT, X, SQUARE
Aggressive Drivers
SQUARE, SQUARE, R1, X, X, L1, CIRCLE, CIRCLE
White Traffic
X, X, R1, CIRCLE, CIRCLE, L1, TRIANGLE, TRIANGLE
Black Traffic
CIRCLE, CIRCLE, R1, TRIANGLE, TRIANGLE, L1, SQUARE, SQUARE
Green Lights
TRIANGLE, TRIANGLE, R1, SQUARE, SQUARE, L1, X, X
Chrome Plated
TRIANGLE, R1, L1, DOWN, DOWN, R1, R1, TRIANGLE
Weather
Sunny Weather
L1, L1, CIRCLE, R1, R1, SQUARE, TRIANGLE, X
Clear Weather
UP, DOWN, CIRCLE, UP, DOWN, SQUARE, L1, R1
Overcast Weather
UP, DOWN, X, UP, DOWN, TRIANGLE, L1, R1
Rainy Weather
UP, DOWN, SQUARE, UP, DOWN, CIRCLE, L1, R1
Foggy Weather
UP, DOWN, TRIANGLE, UP, DOWN, X, L1, R1
Peds
Random Ped Outfit
L1, L1, LEFT, L1, L1, RIGHT, SQUARE, TRIANGLE
Peds Riot
L1, L1, R1, L1, L1, R1, LEFT, SQUARE
Peds Attack You
L1, L1, R1, L1, L1, R1, UP, TRIANGLE
Peds Have Weapons
R1, R1, L1, R1, R1, L1, RIGHT, CIRCLE
Follow Me
DOWN, DOWN, DOWN, TRIANGLE, TRIANGLE, CIRCLE, L1, R1
Bobble Head
DOWN, DOWN, DOWN, CIRCLE, CIRCLE, X, L1, R1
Gameplay
Faster Clock
L1, L1, LEFT, L1, L1, RIGHT, CIRCLE, X
Faster Gameplay
R1, R1, L1, R1, R1, L1, DOWN, X
Slower Gameplay
R1, TRIANGLE, X, R1, SQUARE, CIRCLE, LEFT, RIGHT
Media Attention Meter
L1, UP, RIGHT, R1, TRIANGLE, SQUARE, DOWN, X
Upside Down
DOWN, DOWN, DOWN, X, X, SQUARE, R1, L1
Upside Down
X, X, X, DOWN, DOWN, RIGHT, L1, R1
Display Game Credits
L1, R1, L1, R1, UP, DOWN, L1, R1
Multiplayer
Unlock #1
UP, UP, UP, SQUARE, SQUARE, TRIANGLE, R1, L1
Unlock #2
UP, UP, UP, CIRCLE, CIRCLE, X, L1, R1
Unlock #3
UP, UP, UP, X, X, SQUARE, R1, L1
Unlock All
UP, UP, UP, TRIANGLE, TRIANGLE, CIRCLE, L1, R1