Dominion Tank Police is what happens when you get an entire battalion of guys like this. And in a humorous twist, the most cowboy of the cowboy cops in the squad is the only girl in the squad: Action Girl and Cargo Shipper Leona.
Batou in Ghost in the Shell is a good example for an actually heroic cowboy cop, but the whole Section 9 could fit this trope as well. Even Aramaki and the Major, who are much more sophisticated and less hot-blooded don't have the law very high on their list of priorities. Given the nature of their work, this is to be expected: Being Secret Police rather than regular cops, they have little effective oversight, don't usually need to worry about making a collar that will stand up in court, and are often actively fighting against other branches of the corrupt Japanese military and security apparatus.
"Sleepy" John Estes, the titular Mad Bull 34, always acts in the interest of justice first and foremost. He does this by killing every violent criminal he meets — it's very rare for him to make an actual arrest. His chief thinks he' a disgrace to the uniform and keeps trying to curtail his exploits or get him fired, but Internal Affairs says he's clean (he's not).
One Piece has Captain Smoker, the main protagonist's primary Inspector Javert / Sympathetic Inspector Antagonist. In fact, his tendency for this is implied to be the main reason why he had his rank during the start of the series — Smoker's strength was well beyond that of a captain at the time. Eventually, he gets promoted to Commodore, and then Vice-Admiral, and is still chasing after Luffy.
smoker is also a commander of a marine unit of the 5th grandline marine base, or G5 for short, its were HQ sends all the cowboycops and other overely violent marines, meaning The cowboycop of the series is now Da Chief of a unit composed out of cowboycops
One Officer Jenny in Pokémon. She'll attack you with a bowling ball before sending out her Chatot, buddy.
Hibari in Speed Grapher is a justified version: She gets away with being a Cowboy Cop because her chief is terrified of her. Besides, she doesn't attack people; she self-defenses them.