At the 'Title' screen when 'Start' appears enter the following codes to unlock the corresponding effect in the game. If you have entered the code correctly you will hear a sound as confirmation.
Unlock Super Cars:
Press Up, Left, Right, X, Circle, Square.
Unlock Heavy Metal Cars:
Press L1, R1, L1, Square, R1, Up.
Unlock Bonus Track:
Press X, Up, Triangle, Down, R1, L1.
Unlock Reversed Tracks:
Press Left, Triangle, R1, Circle, L1, Down.
Unlock Super Championship Race:
Press Right, Square, Left, Circle, Up, X.