Invincibility:
Pause the game, go to Options and press Up, Down, Left, Right, Left, Right, White, Black.

Unlimited ammo:
Pause the game, go to Options and press Left, Right, Up, Down, Up, Down, Black, White.

All missions:
At the Mission Select screen, press Up, L, Down, R, Left, L, Right, R, Up.

Thanks to Revolution readers Martin Brodeur and charlielee!