Why hasn't anyone mentioned it yet? People are throwing out names like Call of Duty and Rainbow Six Vegas and yet this one is ignored? Fine, I'll say it!
SWAT 4
You play as a SWAT officer. As an officer of the law, you are not allowed to open fire till fired upon yourself. Your goal is to arrest, rather than slaughter ala Rainbow Six, your opponents. Killing is frowned upon and counted against you at the end of each mission in which a score is assigned based on how well you performed the mission, too low a score and even though you 'beat' the mission, you are still counted as a failure since you repeatedly failed to follow police protocol. Some enemies will give up easily when given a chance, you shout for them to drop the gun and they do so, others will behave erratically if they're a druggie or religious nut for example, and are much less predictable. While others, the hardcores, won't give up till you've brought them down yourself.
One bullet can kill, especially later in the game. Although in early stages when your opponents are mostly gang members, nuts and lunatics wielding crappy little pistols with hollow-point rounds, your armor will prevent much fatal damage. Although a bullet to the face, even from a crappy shot with a pissy little pistol, will still kill. That goes for both the suspects, the allied AI, and YOU! Shots to the leg would slow you down while injured arms would ruin your aim.
You however are urged to use non-lethal means of weaponry, which again is fine when you're going against druggies and gangs wearing t-shirts and jeans all a-begging to be shot with bean-bag shotguns, pepperball rounds, or even tazed. But when you're near the final missions and your opponents are well armed and armored militants with proper training and perhaps even using gas-masks and helmets, suddenly trying to get them down via non-lethal means is a helluva lot harder (And yet all the more rewarding when you do so. In online matches, the sign of a *true* pro wasn't his kill count, but how many arrests they got. Arresting an enemy player was the ultimate insult.)
The mission objectives are rather than one long and silly story, instead a series of escalating unconnected crimes each with their own personal stories and lead-up events which you are free to read up and peruse complete with listenable 911 calls and witness records.
And to boot it was and still is one of the best FPS out there. Extremely fun and also extremely moody. There's a mission where you're sent after a serial-killer that preys on young women and girls... one of the most terrifying and atmospheric levels ever put into a game. Ever!
Multiplayer was also great!