The whole LA Noire style thing seems pretty popular to people here, and it got me thinking just now.
A sandbox detective game where you're a total vigilante. The backstory is that through some convuluted, comicbook like series of events, you lost your family/lover/whatever you had to live for to some horrible crime, and now you seek revenge not only on the dude(s) who did it, but on all crime everywhere.
You start out just beginning your quest of bringing justice to whatever godforsaken crime-riddled city you live in, and the overarching goal is finding out about crimes, and seeing what you can do before the police can, or even while the police are in the middle of their own investigation. You can't become a cop of course, but you can try to befriend one or two and maybe get a contact on the force to help you out, but if you say the wrong thing to a cop, or you go to your contact too frequently and he gets caught giving out information to you that was supposed to remain police business, you'll end up in deep shit as the cops keep a close eye on you for a while after that, so you run a much higher risk of getting caught doing your own vigilante thing.
The detective work itself woudl be similar to LA Noire in some respects, like looking for clues at a crime scene before the cops arrive, but you'll have to hurry because if you get caught at the scene, you could get arrested, or at least become a suspect, which hampers things. (The lesser the crime, the longer it takes for the police to arrive.) If you decide to not take the risk and investigate the crime scene after the police have left, then there won't be as much evidence left to find, which makes your job harder. How you'd actually find out about the crimes is a matter I haven't fuly thought of yet, but maybe you can eventually get a police scanner for your car to make the process easier.
Actually going after the criminal is where you'd really start to veer from LA Noire. Sometimes it'll be a very quick, more action-oriented streetcrime, one that you could even do without the cops on your ass, like chasing down a dude who just beat a guy down and stole his wallet, or stopping a guy who is in the middle of trying to love tenderly a woman, which would be accomplished by using force to subdue the guy, but not excessively or else you get in trouble with the law. The main focus of the game however, would be on more complicated crimes that require quite a bit of time each to solve, but not too much time, or else the police find the guy first, which of course, eliminates your whole vigilante purpose.
Like the police contact idea, you might find some shady underworld kind of guys who you could schmooze, pay, or threaten into giving you info on any significant recent crimes or figures of infamy. If this guy gets exposed as a snitch however, it could mean his death and trouble for you, so like the police contact, you can't rely on him too much if you don't want him to get caught.
Actually finding and dealing with criminals would involve a number of factors. Maybe you're dealing with a total pushover of a carjacker who you could easily take in a fight, but you track him down to a home in a well to do part of town, so there's a higher chance of the cops busting in on you subduing him, depending on how sneakily you get into his house and do so. Or maybe you're tracking down a guy who shot a man, stole his wallet, and then ran back to his house real quick to gather his things before fleeing. Then you not only have to hurry before the cops get there, but, unless you want to keep on his trail for longer, you also have to stop him while he's in the middle of getting ready to run, and at the same time, you'll ahve to take into account the fact that he has a gun, and you may not.
To earn money, maybe you'll put your skills to a bit more legal use, and catch bounties, but those would be far and few between, so relying on that as a sole source of income wouldn't be practical. Less legal ways of earning money could mean anything from being a bodyguard to killing a rival crimelord, but, even if you're working for a scumbag, There would be no jobs where you do anything that is truly 100% immoral. You can torture a criiminal to death, but not an innocent person. You can't do any arms deals or drug deals, but you can crash them and kill everyone involved. I know there's certainly a thin line in all of that somewhere, but basically, if you can't find even the flimsiest justification that matches your code of justice, then you literally cannot do whatever it is you're trying to justify.
Going on this, ther would also be a sort of combined morality/reputation system that would vary on how you dealt with criminals, and just who the criminals were. Maybe you're a ruthless Frank Castle kind of guy who likes torturing the wicked to death. That's all well and good for catharsis, but if the punishment you dish out is far too harsh for the crime (Like say, bludgeoning a guy to death for pickpocketing) then the public will react with horror and you'll run the risk of getting caught by the cops, and getting imprisoned for murder would pretty much mean game over (Unless maybe you get out of custody and spend the rest of that save file on the run.) On the other hand, maybe you're a more noble Batman guy, who simply subdues criminals for the cops to find. The public eye will look at you with more appreciation, and there'll be less heat from the cops, but it won't bring you as much noteriety as more outrageous actions, and noteriety would still be important, as it would mean more contacts, and opportunities to get paid. Overall, I would imagine that leaning more towards Batman would be better in the long-run than leaning towards The Punisher, but that's okay, because Batman is fucking awesome.
The last major thing that I can think of adding is to that whole reputation idea. If you happen to take down a guy who belongs to a crime family, then that crime family might decide to try and rub you out. Maybe they'll start by sending hit squads that you easily kill before they've even started tracking down, but be warned, as the more heat you build up, and/or the more of a ruthless scary bastard you are, the more likely it is that they'll send a guy who's just as ruthless and scary as you are, and possibly even moreso. On the other hand, if the crime family you're dealing with doesn't have much power, maybe it's just a kind of big street gang, then doing enough to them will cause them to back off and refrain from as much criminal activity, which helps build your noteriety and gives you more job opportunities.
I just got this idea about an hour ago, so I know there's probably numerous flaws with it, but I think it may just be possible, if extremely difficult to make into a real game that would contain enough of these elements for people to want to play it.
Oh, one more thing, if you do enough Batman-y things (crashing in through windows before subduing crooks in hand to hand combat, running and jumping across rooftops in the dark of the night, getting the police to actually make a signal for you.) Then you're rewarded a Batman mask for your guy to wear, and his voice gets replaced by Christian Bale's Batman voice.