Invinciblility:
At the main menu press L1, TRIANGLE, R1, TRIANGLE, DOWN, DOWN, CIRCLE 

Better AI:
At the main menu press TRIANGLE, RIGHT, LEFT, SQUARE, UP, CIRCLE, DOWN, RIGHT 

Easy Trophies:
At the main menu enter one of the following codes - 

Beginner: RIGHT, RIGHT, L1, TRIANGLE, TRIANGLE, R1, RIGHT
Intermediate: RIGHT, RIGHT, SQUARE, LEFT, L1, R1, SQUARE, SQUARE
Expert: RIGHT, RIGHT, CIRCLE, LEFT, L1, CIRCLE, R1, CIRCLE 

Unlock Championships:
Enter these codes at the main menu - 

Intermediate: DOWN, SQUARE, UP, SQUARE, RIGHT, RIGHT, LEFT
Expert: TRIANGLE, RIGHT, LEFT, SQUARE, UP, CIRCLE, DOWN, RIGHT 

Unlock Crash Arena:
Enter the following codes at the main menu - 

1 Player: LEFT, RIGHT, RIGHT, SQUARE, DOWN, TRIANGLE, TRIANGLE, SQUARE
2 Players: RIGHT, LEFT, LEFT, CIRCLE, UP, TRIANGLE, TRIANGLE, SQUARE.