Enter the following at the Load Game menu.

Invincibility:
Press Up, Down, Left, Right, Left, Left, Right, Right, L, L, R, R, White, Black

Unlimited ammo:
Press Up, Right, Down, Left, Up, Right, Down, Left, L, R

Level select:
Press X, X, X, B, B, B, Y, X, Black, Black, White, White

Big heads:
Press Right, Up, Left, Down, Right, Up, Left, Down, Right, L, R, L, R

All instant action levels:
Press Up, Down, Left, Right, L, R, L, R

All planes and missions:
Press Y, Y, Y, X, X, X, L, R, Black, Black, White, White

All environments:
Press Down, Up, Up, Down, Left, Right, L, R, L, R

More instant replay views:
Press Up, Down, Left, Right, R, R, L, L

Dornier 335:
Completely finish the game (complete every secondary and bonus objective in each level).

X-Wing:
Beat every campaign and challenge mission.

TIE Fighter:
Beat every campaign and challenge mission.

Thanks to Revolution readers Pie in the Box and Bobby Jo!