Parodius

All items:
Pause game play and press B(2), X(2), A, Y, A, Y, Up, Left.

Invincibility:
Pause game play and press L, R, Up, X, right, A, Left, Y, Down, B, A, Y, A, Y, r.

Three smartbombs:
Pause game play and press X(3), B(3), Y(3), A(3), L, R.

Level Select:
press Up, right, Down, Left, X, A, B, Y at the options menu.

Auto-pilot:
Pause game play and press Up(2), Down(2), L, R, L, R, B, A.

Control red octopus:
Wait until the penguins that located before the red octopus appear.
Stop, then press Up + L, B(5), Y(5), A(5).
When the red octopus appears, press A +  Y.
The position and size of the red octopus may now be changed with the D-pad.

Disable cheats:
Pause game play and press Up(2), Down(2), L, R, L, R, B, A.