How about the player being a demi-god who has his god-like strength reduced by the powers-that-be every time he takes a life. In order to save the humans he lives amongst from some terrible evil, he needs to go off on quests to defeat powerful enemies which obviously comes at a price.
Such a game would involve trying to avoid confrontations as much as possible by sneaking around (think the Thief series) and even running and hiding (Amnesia?) so you can avoid having to kill the lesser bad guys. Killing the bosses would presumably be unavoidable.
In such a scenario the protaganist would likely favour weapons that are less likely to kill, like a staff or a war-hammer, and maybe a slingshot. And how about some fire-weapons similar to molotov-cocktails, that can be used to prevent enemies following you down a corridor.
There could be a scenario where you sneak into some castle and kill some boss in a one-on-one fight, but all the guards you sneaked past then get alerted and to get away some enemy deaths are unavoidable, resulting in your powers being greatly reduced.
The ultimate boss can be a human who's power comes from the army he commands. Maybe it's the emperor of the lands or something, but in the finale when you have no more god-like powers, he thinks he can defeat you in a one-on-one fight. It would be kind of similar to the ending of The Gladiator, where the emperor thinks he can defeat a near-death Russel Crowe!