Fun cheats that have no effect on the game (eg big head mode, costume swaps, making guns look like dildos without effecting them in any other fashion) should be more common - some people will like them, some won't, and the ones the don't can simply ignore them. Cheats that have a more substantial effect (eg infinite ammo or invincibility) can be a lot of fun too, but should be restricted to single player where again it is up to the player whether or not they will enjoy using them. Obviously they would have to not count towards trophies/achievements or the achievements would become basically worthless. One problem with the few games that do include these is they often interfere with saving, which is a pain - I should be able to have say one serious file where I am actually working towards the story and an alt-save where I am manically blasting everything with moves with unlimited ammo in that superweapon that is crazy fun to use but overpowered, so they made ammo really scarce. Finally multiplayer should not have cheats per se, but mods that effect the gameplay for everyone (think the mutators from unreal tournament). Simply list the effects that are modifying the map on the lobby screen so that people wanting to play an instgib match can do so, people that enjoy low-grav capture the flag can do their own thing, and people that prefer just plain ol' vanilla gameplay can do that too.
Wow. Wall of text out of nowhere.