Enter the following at the Main Menu:

Invincibility:
L, R, L, R, L, R, L, R

Level Select:
X, Y, Z, Z, X, Y, Z, Z

Liquid Metal Mode:
B, Y, X, B, Y, X

Big Head Mode:
R, R, L, R

Tiny Heads Mode:
L, L, R, L

Flame on:
X, Y, B, X, Y, B

Enemies Punched Are Set On Fire:
L, L, B, Y, L, L

Bullets Explode:
L, R, Z, Y, B

Slower Enemies:
B, X, Y, Z, L, R

Thanks to Revolution readers eos and Martin Brodeur!