Invincibility:

While playing the game, press Square, X(2), Square, Triangle(2), Square, Circle(2), Square, R3. If you entered the code correctly, you will hear a sound. Although you will lose health you cannot die.

Infinite rage:

While playing the game, press Triangle, Square(2), Triangle, Circle(2), Triangle, X(2), Triangle, R3. If you entered the code correctly, you will hear a sound.

Faster enemy reflex:

While playing the game, press X(2), Square(2), Triangle(2), Circle(2), Triangle(2), Square(2), X(2), R3. If you entered the code correctly, you will hear a sound. You will gain double reflex with every kill.

Classic Wolverine (blue/yellow) costume:

While playing the game, press X, Square, Circle, Square, X, Triangle, X, Triangle, X, Square, Circle(2), Square, R3 to unlock Wolverine's classic blue and yellow costume. If you entered the code correctly, you will hear a sound. Then, exit to the main menu, and switch costumes.