You control Karma and make sure people reap what they sow.
ideas suggested:
you're really small
you get bigger as the game progresses
as you move on you get powers
sometimes you have to blend in with your surroundings
you have a limp button, where you become limp like a doll to avoid attention
you make people pay in ironic ways to make sure karma comes full circle
you can stress a man out until he has to get a smoke, but his gas line is broken
Since karma is the idea of "Do evil and the evil will eventually come round to you," (condensed, obviously, it's a lot more complicated than that) I personally think that the killing of pets will detract from the meaning of what you're supposed to be doing. The pet hasn't done evil, the master has, so the pet doesn't deserve any evil to be done to him.
I'd therefore suggest that killing or harming the pets in any way results in some kind of score penalty when the mission is completed. Non-lethal or non-painful methods to remove the obstacle, such as luring a dog outside a house and then blocking the dog door up with something or popping one of the master's sleeping pills into a cat's food when he's not looking, or simply avoiding the pet outright would, obviously, not be punished, though they would be a lot more difficult to do.
I'm now thinking that, if the player character is doing inherently evil things without the justification that it's an evil individual he's doing it to, maybe he could then be attacked by another Bad Karma out to get him? Maybe just an alternate ending or something, since I don't know how that would be implemented.
I suppose that would suggest that Karma is a collective, some kind of spiritual organisation featuring numerous Karmic Agents... I dunno, I'm thinking backstory and storyline here and we haven't really entered that territory yet. Assumedly the player character must be reporting to someone in order to get information at the start of the mission regarding the target, unless it's done in a similar way to The Art of Theft where the beginning of each mission is a short monologue where the character lists his thoughts on the task at hand.