Cheat mode:
At the main menu, highlight Options Mode and press Down, then press Left or Right until "Option: Cheat Codes" is selected. Press X and then enter one of the following case-sensitive cheat codes, which work in Arcade mode:

dextran                 All modes
Globetrotter            All cities
theCollector            All cars
pennyThug               All areas and cars

rimbuk                  All areas and cars 

immortal                Guns, rockets, nitrous and no damage
carcrobatics            More control in air

savethekids             Rocket and guns - press R3 and L3 to use 

gladiator               No damage

greenLantern            Infinite nitrous

howhardcanitbe(0-9)     Change Career mode difficulty (0 is easiest, 9 is hardest)

LAPD Car:
Beat all 5 L.A. Arcade circuit races.

Paris Cop Car:
Beat all 6 Paris Arcade circuit races.

Tokyo Cop Car:
Beat all 7 Tokyo Arcade circuit races.

Rocket Car:
Beat the game 100%.

Thanks to Revolution readers Andy, minkis, CamaroCop21, Punk Monkey, jeremy, Jalil Samir Abushanab, DARIUS, Silver_Ninja, JHeustis, PhoEniX, RapcityZ and PheOniX!