Automatic Rapid-Fire
For a continuous burst of fire power, press Up, Up, Down, Down, Left, Right, A, A, B, B, C, C at the title screen.
Unlimited Continues
At the title screen, press Up, Right, Down, Left, A, B, C, U, Left, Down, Right. If you did this correctly, the "Continues Left" counter will read "FREE PLAY" when you lose your first ship.