A murder simulator. Nothing arcadey. Not Hitman where it's a kill or be killed scenario. Not a GTA where it's arcadey and "lol". A murder simulator in a city.
When you start the game you get to choose everything about you. Age, history, occupation, sex, appearance, etc. And, from there, you can do whatever. The goal would be to last as long as you can without being caught, which could be forever. You could just murder one person and do away with the body perfectly, you could kill thousands of people and leave behind tons of evidence but be untraceable. You could also just throw a grenade in to a crowd and be shot down/arrested.
You'd also be awarded points for following some sort of pattern. For example, murdering blonde haired women in their 20's, or obese men.
Maybe you could be awarded points for originality, brutality, or quickness. All sorts of stuff you could do.
I think that would be more controversial than anything else.