Purna in Dead Island was one of these in her backstory. Fed up with the racism (she's half-Aboriginal), sexism, and corruption in the Sydney Police Department, she eventually snapped, confronting and shooting a child molester who had used his wealth and connections to escape prosecution. She later became a Bodyguard Babe for rich VIPs.
In Deus Ex, Anna Navarre's preferred method of law enforcement is to sneak in and kill everything in sight. She was the reason why you didn't go back to Unatco without pay during the Battery Park Mission is because she wrote a good report for you and claimed the NSF were beyond negotiation.
In fact, that is UNATCO procedure on the ground level, most of the troops wants to shoot first and ask questions later. Even if it means racking up a huge civilian bodycount.
" You got the right idea. Cap the bastards before the lawyers get involved."
As pictured, there exists an Atari Lynx game titled Dirty Larry: Renegade Cop which runs the gamut of cop thriller cliches. Larry's hands are glued to his pistol and he never makes legitimate arrests.
In Dragon Age II Aveline is forced to become one of these early on when it becomes increasingly clear that Kirkwall's City Guard is corrupt. After removing the root cause of the problem Guard Captain Jeven, she gets promoted to the vacant position. Even then, she still takes time off from her duties to go adventuring with Hawke and makes allowances for some of her less than law-abiding companions (Merrill the apostate blood mage, Anders the apostate abomination, and Fenris the squatter).
Fallout 3 had an entire organization of cowboy cops that the player could join: The Regulators.
Sonora Cruz We've dedicated our lives to bringing the evil to justice. And out here in the Wasteland, there's only one brand of justice: the gun.
In Fallout: New Vegas, you have the option of installing one of these as the Sheriff of Primm. He's found in a nearby jail, having been arrested for being a Cowboy Cop back in NCR territory, though he played no part in the Powder Gangers' uprising. In the epilogue, it's stated that while he is fair for the most part, occasionally a few people will wind up dead with little to no evidence against them.
Role-playing games generally have a shortage of cowboy cop types. The closest the Final Fantasy series has come up with might be Fish out of Temporal Water Tidus (Final Fantasy X). He gets shoehorned into becoming a Guardian for the Summoner, primarily because he has no other livelihood or hope of navigating an alien future where his celebrity is long forgotten. His ignorance proves to be a real asset, however, as the church of Yevon is completely foreign to Tidus; thus, it inspires no fear in him. He bucks the system at every turn, is branded a blasphemer, and eventually convinces the Summoner and his fellow guardians to disown the church. Worst guardian ever... or the best!
Garrus Vakarian, although considerably more polite and soft-spoken than is usual for the trope, is certainly one. In his very first appearance, he is arguing with Executor Pallin over his most recent investigation, and throughout the rest of the game he's a frequent supporter of killing criminals rather than giving them the chance to escape justice. He also is a deconstruction of the trope because his Cowboy Cop urges are not tolerated by C-Sec. As such, a Paragon character can rein him in and teach him that it's important to do things the right way, not just get them done. Although it doesn't end up sticking completely — even if you took this route with him, he's become a vigilante by Mass Effect 2, which he will apologise for. In fact, Garrus even admits in Mass Effect 2 that he isn't a very good turian, because of his refusal to obey orders if he feels the order is unjust.
Renegade Shepard can be this. In fact, C-Sec generally doesn't like Spectres because of the risk of them becoming this.
Captain (later Commander) Bailey of C-Sec is more of an Old-Fashioned Copper, but he certainly doesn't have a problem with bending or breaking the rules.
In the Citadel DLC of the third game, it's shown in a video archive of historical events that the first Spectre was a Salarian operative of some sorts who used 30 civilians to bait and flush out his target.
Max Payne - Though, Max's idea of police work is pretty flimsy: If he isn't investigating the crime scene, he is making it. Lampshaded by Max himself in one of the cutscenes:
"Collecting evidence had gotten old a few hundred bullets back."
Metal Gear's Solid Snake didn't have much of a personality to begin with. He evolved into a gruff ex-solider with a chip on his shoulder who just wants to race sled dogs in peace. Following Metal Gear Solid, Snake defies orders and exposes the Shadow Moses conspiracy, completely torpedoes the Presidency of George Sears, then goes into hiding to covertly sabotage his own nation's variations on Metal Gear weapons.
Fridge Brilliance dictates that the Flat Character of early Snake is attributed to his naiveté and blind obedience to orders. Later games paint him as much more jaded and anti-authortarian.
Metroid - According to a prequel manga, this was the occupation of Samus Aran before she became a bounty hunter, then savior of the universe. In Metroid Fusion, where Samus is revealed to hate following orders and ends up disregarding them entirely to eliminate the threat. And given that when the Federation saw a being with equal firepower to Samus at her strongest, who blasted its way out of top-security quarantine, can reproduce through mitosis and have ten of itself running around (at full power) in a matter of minutes, can assimilate anything that isn't Samus by touch, and wants to spread the X throughout the galaxy Zerg-style, they wanted to capture it alive, it's probably a good thing Samus didn't play along.
Ex-Marshal Anderson from Outlaws is an interesting example. He gunned down a suspect in cold blood, was called out on it, and was fired. However, when we meet Anderson, he fully accepts that it was right to fire him and that officers of the law have to follow the law, and is very quick to put down anyone who says otherwise.
Case 5 of Phoenix Wright Ace Attorney features Jake Marshall, a cop who's dedicated himself to finishing his personal investigation of his brother's murder, no matter what rules he has to break or who he brings down. He also wears a poncho and ten-gallon hat, decorates his office with cacti and speaks in a 19th-century Western dialect, all for no reason that anyone can figure out, making him both an example and a parody of the trope. He's not even from Texas.
Ace Attorney Investigations plays with this with Detective Tyrell Badd, who despite his badassery tends to obey orders and do things by the book even when he finds it distasteful. Except for that whole Yatagarasu thing.
In SWAT 4, acting like you are in Rainbow Six or Ghost Recon where you shoot the criminals without them firing back can get you plenty of "Unauthorized use of Lethal Force". in the elite difficulties, this hits even harder as the death of more than 2 suspects is an automatic mission failure.
Mocked in a Heavy update for Team Fortress 2. After eating a sandwich (long story), the Heavy sometimes says, "You're a loose cannon, sandvich, but you're a damn good cop!" Made hilariously literal here.
Velasquez of Traffic Department 2192 takes this trope and runs with it. She has no sense of professionalism, displays no concern for protecting the innocent, disobeys orders in order to kill more baddies, and primarily interacts with her colleagues and superiors through Ineffectual Death Threats (or effectual death threats.) Yet she can face twenty better-armed opponents and kill them all, and until such time as order can be restored her superiors have no choice but to keep her around, no matter how much they hate her guts.
True Crime: Streets of LA opens with Nick Kang coming back from suspension for his Cowboy Cop antics. It is his shoot-first-ask-questions-later nature that gets him invited to join the Elite Operations Division: to get the kinds of crooks the EOD goes after, it takes cops that aren't afraid to bend, or even break, the rules.
According to the backstory of Mega Man X, Vile was one when he was still with the Hunters, to the point where he wound up being locked up before Sigma went crazy and freed him. The Archie comics show what he did to cross the line: collapsing a highway overpass on top of a recently reactivated Wily Machine. While civilians were still driving on it.