Well, that didn't take long. GameFAQ has already posted the first batch of cheats for Saints Row: The Third.
Here's is the current list of cheats:
brains = peds are zombies
hohoho = peds are pimps and prostitues
mascot = peds are mascots
givevortex = Vortex
givespecter = flying bike
givevtol = F69 Vtol
givevulture = saints' helicopter
givecyber = Cyberdestructor
givegrenade = Grenade
givechainsaw = chainsaw
giveminigun = minigun
givemolotov = Molotov
giveairstrike = air strike
givedrone = Drone
giverpg = rpg
givesatchel = satchel
givekrukov = K-8 Krukov
giveultimax = As3 Ultimax
givehammer = hammer
givetek = Tek z-10
givekobra = Kobra Ka-1
giveapoca = apocafists
goldengun = one hit kill
It's worth noting that when you use cheats on Saints Row III, they disable achievements.
Saints Row: The Third will be hitting store shelves tomorrow, November 15th, and I personally cannot wait to cause insanity and mayhem in that game. These cheats will undoubtedly help me achieve that.