Crackdown definitely fulfills this wish. For those of you who haven't heard of this game by now: It is more or less a GTA(<=3) on steroids (or gen-therapy) where you for once are some kind of super-cop being created by a global police force in order to fight gang-/organized crime. The whole super-cop things enabled you to improve your character's skills by simply shooting bad people, exploding stuff, driving over bad people (to improve your driving skills) and so on.
You have 5 skills you can improve on:
Besides going the obvious way when it comes to increasing these skills (by driving, shooting etc.) there are also 500 so-called ability orbs hidden all around the city which are the fastest way to increase your agility skills. Then there are IIRC 300 hidden orbs that increase all of these skills in parallel. Searching for all of these is really a great way to play this game for ages :)
You can now use those skills in the 3 districts of the fictive city of Pacific City which are ruled by latin american, russian and chinese gangs respectively which all have different cars (to highjack) and different ammunitions (to use for yourself). And your job is, to destroy those gangs. The order in which you proceed is completely up to you and it definitely influences how the game feels.
For example: You could start with the latino gangs which mostly rely mostly on submachine guns and pump-guns and are therefor the easiest enemies. Or you could make a small trip for example to the chinese gangs and get yourself a nice heat-seeking rocket launcher.
In all districts you have more or less 2 objectives: Conquer some supply points which are basically your re-spawn points and also offer you a safe place to get new ammo and change your weapons (as soon as you've once brought them there first). And second to kill key members of the respective gang. Also here the order influences your experience. For example if you kill the recruiting expert first, you will meet less enemies. If the weapons expert is your first target, the enemies will have weaker guns and so on.
And let's stick with weapons for now: As already indicated the game has a wealth arsenal of firearms and explosives thanks to the 3 different gangs. But also the handling of these weapons is very simple and hitting enemies isn't really hard work as it was in the GTAs. First of all, the game features well implemented auto-targeting which lets you aim at the nearest enemy by just hitting and holding LT. When someone got targeted, you can also select different body parts in order to inflict precise damage (not really useful in my opinion apart for the headshots, but nice anyway). The only problem this system sometimes has, is that in the heat of the battle you will often target foes, that are already down. While sometimes annoying it probably won't ever put you into virtual-life-threatening situations.
The unique aspect of Crackdown is the style in which you do all this. Thanks to you being a genetically manipulated/created human, you can (after increasing your respective skills) for example jump many many meters high and lift cars and through them at enemies. This new sense of freeness feels absolutely great. You can easily get on nearly every rooftop and operate from there. This way you can also get around most of the bosses' guards if you want.
So the game is quite on the brutal and straight forward side, but still isn't a splatter-movie thanks to the cell-shading look. And the graphics are really nice in the sense that if you find a spot high enough, you can see from one end of the city to the other and there are rarely and popups that you really notice. On the other hand while there are quite a few NPC models on the streets, there are IMO still too little and they all act too much alike for my taste.
Another problem the game for me had, was that you move from "mission" to "mission" only thanks to your own scouting and to intel provided by your agency. You will never find a document, a computer terminal to hack or something like that. This gives the whole city just the feeling of a playground for someone who knows everything anyway. Too bad, some information items would have improved this game even more :-)
Some reviews also criticized, that the game is more or less lacking a story. This is definitely and apparent esp. when you consider the basically completely lacking NPC-interaction. But for me personally this wasn't really a problem since I consider this game more as a sandboxy platformer with guns... And has Mario really a story that is worth mentioning? ;-)
Just a few last words about the sound of the game. Good weapons sounds, but only mediocre localization. Esp. the German localization of "Skills for kills" is kind of ... well, perhaps it was the last sample they had to translate.
Another problem was the very low number of speech samples, meaning that you will here everything nearly as of as Ryu's Hadoken.
I guess I really can't write enough about how much fun it is to have the amount of freedom Crackdown offers thanks to your super-human abilities, but the game also has some week spots when it comes to the story and also to the the interaction with NPCs. "You can hurt them" more or less sums all your possible interaction up. So what you get is a fast-paced action game orienting itself definitely on the GTA series but with a well implemented targeting system, good graphics, good soundtrack and enough goodies to keep you occupied for well beyond the 10h it at max. takes to complete the campaign.