All Cars & Levels:
Pause the game and press L2, R2, R2, L2, R1, L2, L1, Left, Right, L2, Down, R2. Repeat this code to disable it.

Increase Speed:
Pause the game and press R1, L1, L2, R2, Right, Right, Right. You can go even faster by entering the code again.

Weightless:
Pause the game and press L1, R2, R2, L2, R2, R2. This code only works for player one, even in multiplayer.

No Gravity:
Pause the game and press R1, R2, R1, R2, Up, Up, Up.

Matrix Mode:
Pause the game and press R2, L2, L1, R1, Left, Left, Left. Use this code to slow everything down.

Invisibility:
Pause the game and press R1, L1, L1, R2, L1, L1, L2.

Unlimited countermeasures:
Pause the game and press R3, R3, R3, R1, R1, R2, R2. Repeat this code to disable it.

Hints

What You Unlock By Beating Missions:
Beat the missions listed to get the corresponding prize:

Super Buggy: Available at beginning of the game 

Super Buggy Boost: Mission 3

D-5 Hondo: Training Mission 3

D-5 Hondo Oil Slick: Mission 8

Baja Truck: Mission 4

Baja Truck Bombs: Mission 7

ATV Monster: Mission 10

ATV Monster's Speed Burst: Mission 14

Du Monde: Mission 13

Du Monde Oil Slick: Mission 21

Sahara Special: Mission 17

Sahara Smoke Screen: Mission 18

Grenadier: Mission 24

Grenadier Bombs: Mission 25

Kavostov Halftrack: Mission 27

Kavostov Halftrack's Smoke Screen: Mission 29

Vietnam Map: Mission 9

Georgian Russia Winter Map: Mission 22

Thanks to Revolution readers the crook, Mystery Man, Joseph B. Winkle, Anthony, Jason, Rupheas Exavier Sasparilis, Joey, and auxiliary!