Enter the following at the 'Cheats' screen:

EMERPUS    Invincibility 
FMNFB      All cheats shown + big head
TEXAS      All weapons for level 
MADMAN     Unlimited ammo
SELLOUT    Level select 
SLLEWGH    Invisibility 
HEID       Big heads
ZOO        Zoo mode (kill any animal with war club)
HUNTER     Unlock Demo mode and Target mini-game

Thanks to Revolution readers gabriel cardona, Black Jeebus, Fred Shaw, Chris and Dave!