Invincibility:
In the Cheat menu type Left, Square, Up, Triangle, Right, Circle, Down, X.

Invisibility:
In the cheat menu type Left, Square, Right, Circle, Left, Square, Right, Circle.

Slow-Motion:
In the cheat menu type Right, Square, Up, Triangle, Right, Square, Up, Triangle

Unlimited Ammunition:
While in the game type Down, X, Left, Circle, Down, X, Left, Circle.

Infinite Ammo:
While in the game press pause and type Down, X, Left, O, Down, X, Left, O.

Xen Gravity:
While in the game press pause and type Up, Triangle, Down, X, Up, Triangle, Down, X.

Alien Mode:
While in the game press pause and type Up, Triangle, Up, Triangle, Up, Triangle, Up, Triangle.

Thanks to Revolution reader MudDustKnot!