All power-ups #1:
Pause the game and press Up, Up, Down, Down, L, R, L, R, B, A, Start. After a certain number of times, your ship will self-destruct.

All power-ups #2:
Pause the game and press Down, Down, Up, Yp, Right, Left, Right, Left, A, B, Start. Each time you do this you'll lose one life.

Self-destruct:
Pause the game and press Up, Up, Down, Down, Left, Right, Left, Right, B, A, Start.

Thanks to Revolution readers Brad Priddle, Frankie45 and Wizard of Odd!