Enter the following at the Load Game menu.

Invincibility:
Press Up, Down, Left, Right, Left, Left, Right, Right, L1, L1, R1, R1, L2, R2

Unlimited ammo:
Press Up, Right, Down, Left, Up, Right, Down, Left, L1, R1

Level select:
Press , , , , , , , , R2, R2, L2, L2

Big heads:
Press Right, Up, Left, Down, Right, Up, Left, Down, Right, L1, R1, L1, R1

All instant action levels:
Press Up, Down, Left, Right, L1, R1, L1, R1

All planes and missions:
Press , , , , , , L1, R1, R2, R2, L2, L2

All environments:
Press Down, Up, Up, Down, Left, Right, L1, R1, L1, R1

More instant replay views:
Press Up, Down, Left, Right, R1, R1, L1, L1

Dornier 335:
Completely beat 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!