Pause the game and enter the following:

Big feet:
Right, Right, Right, Left, Right, Left, Right, Left, Left, Left.

Big gun:
, , , , , .

Skeleton:
Left, Left, Left, Right, Left, Right, Left, Right, Right, Right.

Explosive crossbow:
Left, Right, Right, Left, , , L2, R2, , , Left, Right.

Explosive sniper:
L2, R2, Right, Right, Left, Left, Right, Right, R2, L2, , .

Missile crossbow:
Right, Right, Left, Left, L2, L2, R2, R2, , , , .

Missile sniper:
Square, Left, Right, L2, R2, Right, , R2, R2, L2, Left, Left.

Half damage:
, , , , Left, Left, Right, Right, , , , .

No bullet damage:
Left, Right, Right, Left, , , , Square.

One hit kills:
Circle, Left, Right, Right, Left, , L2, R2, , , .

Unlimited bullets:
Square, , , , , , , , Left, , , , , , , , Square.

Unlimited health:
Left, Right, Right, Left, Left, Right, Right, Left, Left, Right, Right, Left, , .

Unlimited Spy Cam:
Left, Left, Right, Right, R2, R2, L2, L2, , , , .

Unlimited TOC:
, , , , Left, Right, Right, Left, L2, R2, L2.

Level skip:
L2, , L2, , L2, Left, L2, Right, L2, R2, R2, , R2, , R2, Left, R2, Right, Square.

Level completion codes must be entered within the corresponding level to work.

Bank level completed:
R2, L2, , , Left, R2, Left, Left, , , .

Carmen level completed:
R2, L2, Right, Left, Left, L2, R2, , , , R2.

Forsythe level completed:
L2, L2, Right, Right, Right, L2, R2, , R2, , R2.

Installation K level completed:
R2, L2, , , Left, L2, L2, , , L1, .

La Casa level completed:
R2, L2, Right, Left, Left, L2, R2, , , , R2.

Magyar level completed:
R2, , , Left, Left, L2, R2, Right, , Right, Right.

Mod level completed:
R2, L2, Right, R2, Left, , R2, , Right, Right, Left.

Museum level completed:
L2, L2, Right, Right, Right, L2, R2, , R2, , R2.

Reliance level completed:
R2, L2, Right, Left, R2, L2, Right, , , , .

Silo level completed:
R2, L2, Right, Left, Left, L2, , R2, , , .

Training level completed:
Left, Right, Right, Left, , , R2, L2, , , .

Thanks to Revolution readers ToriX, dave_dave, Sanchez, and Tiny P!