Pause the game and enter the following:

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

Big gun:
X, X, X, X, Y, Y.

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

Explosive crossbow:
Left, Right, Right, Left, X, Y, Black, White, X, Y, Left, Right.

Explosive sniper:
Black, White, Right, Right, Left, Left, Right, Right, White, Black, X, Y.

Missile crossbow:
Right, Right, Left, Left, Black, Black, White, White, Y, Y, X, X.

Missile sniper:
X, Left, Right, Black, White, Right, X, White, White, Black, Left, Left.

Half damage:
X, X, Y, Y, Left, Left, Right, Right, Y, Y, X, X.

No bullet damage:
Left, Right, Left, X, Y, X.

One hit kills:
Y, Left, Right, Right, Left, Y, Black, White, Y, X, X.

Unlimited bullets:
X, Y, X, Y, X, Y, X, Y, Left, Y, X, Y, X, Y, X, Y, X.

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

Unlimited Spy Cam:
Left, Left, Right, Right, White, White, Black, Black, X, X, Y, Y.

Unlimited TOC:
Y, Y, X, X, Left, Right, Right, Left, Black, White, Black.

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

Level skip:
Black, X, Black, Y, Black, Left, Black, Right, Black, White, White, X, White, Y, White, Left, White, Right, X.

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

Bank level completed:
White, Black, X, Y, Left, White, Left, Left, X, Y, X.

Carmen level completed:
White, Black, Right, Left, Left, Black, White, X, X, X, White.

Forsythe level completed:
Black, Black, Right, Right, Right, Black, White, X, White, X, White.

Installation K level completed:
White, Black, X, X, Left, Black, Black, X, X, L1, X.

La Casa level completed:
White, Black, Right, Left, Left, Black, White, X, X, X, White.

Magyar level completed:
White, Y, Y, Left, Left, Black, White, Right, X, Right, Right.

Mod level completed:
White, Black, Right, White, Left, Y, White, Y, Right, Right, Left.

Museum level completed:
Black, Black, Right, Right, Right, Black, White, X, White, X, White.

Reliance level completed:
White, Black, Right, Left, White, Black, Right, X, Y, X, Y.

Silo level completed:
White, Black, Right, Left, Left, Black, Y, White, X, X, X.

Training level completed:
Left, Right, Right, Left, Y, X, White, Black, Y, Y, X.

Thanks to Revolution readers JØSH and Philo!