Rabid Cop

FBI Agent Norman Jayden: Blake, you are an unbalanced, psychopathic asshole!
Lieutenant Carter Blake: I'll take that as a compliment.

—Heavy Rain

The Rabid Cop is a specific character in police procedural shows who's usually the most prominent portrayal of Police Brutality in fiction.

They might be casually dirty, overbearingly psychopathic, or anywhere in between, but they all have two things in common: a ruthless disregard for civil rights, and an unwavering conviction that any person they've identified as "the perp" really is a perp (regardless of any contradicting evidence) and deserves to suffer. In a Good Cop, Bad Cop routine, they usually take the "Bad Cop" ball and run clear out of the stadium with their torture methods. Likely to be on the emphasis of the "Bad Cop" part in the Bad Cop, Incompetent Cop setting.

Compare Sociopathic Soldier, a person in the military who commits war crimes. Contrast the (presumed) moral Cowboy Cop.

Examples of Rabid Cop include:

Film

Steve Pruitt in Bad Lieutenant: Port of Call New Orleans is Terrence McDonagh's partner who threatens Dub with a beating in the interrogation room. And McDonagh starts to turn into a violent person himself as his addictions spiral out of control.
Van Stretch from Internal Affairs is Dennis Peck's partner who assaults a drug pusher and his girlfriend for resisting arrest.
- Peck is also implied to be disliked by his fellow officers, due to his unscrupulous methods during his job.
Officer Curtis Mooney in Killer Klowns From Outer Space is a misanthropic police sergeant who has to be almost physically restrained by Dave Hanson from beating up two teenagers whom he brought in for public drunkenness. He later arrests Jumbo (unbeknownst to him, is actually a Klown instead of a prankster in a costume) for pranking him with a bunch of water squirting flowers, and later hits the Klown's head with a flashlight, which turns out to be not such a hot idea.
Park Doo-man and Cho Yong-koo from Memories of Murder are a duo of detectives who both uses brute force against suspects, one of whom was a mentally handicapped young man, and get very few results. They're contrasted with Seo Tae-Yoon, who uses logic and reason in his investigation. Though he eventually loses his temper after his frustrations gets the better of him and nearly shoots a factory worker.
Alonzo Harris from Training Day is a rogue narcotics detective who had terrorizes his neighborhood with his controversial and radical methods. He is also just a sociopath who has no qualms about abusing his suspects.
Transformers: Barricade is portrayed as a "bad cop" cliche when he interrogates Sam Witwicky in an attempt to find where are his great-great-grandfather's glasses for the coordinates of the AllSpark.

Barricade: ARE YOU USERNAME "LADIESMAN217"?!?!

David Kujan is a U.S. Customs Special Agent who yells at Verbal Kint several times in The Usual Suspects.

Verbal Kint: The DA gave me immunity.
David Kujan: Not from me. You get no immunity from me, you piece of shit.

Literature

Discworld: "THAT! IS! NOT! MY! COW!". Commander Sam Vimes tries to do the best he can not to turn into a psychopath. Though he also actually has a Vimes-esque entity in his mind to prevent him from succumbing to the darkness.

Sam Vines: Who watches the watchman? I do.

Stephen King's Desperation: Collie Entragian. Of course, I'm going to kill you not all he seems, I'm going to kill you this being a Stephen King novel. I'm going to kill you.
Rudolph in The Dresden Files is a corrupt Chicago police officer obsessed with stirring up trouble in the Special Investigations unit, due to his grudge against Harry Dresden. In Changes, when he tries his best to play the Bad Cop, his desk-pounding and spittle-flecked screaming manages to do is cause Harry to crack up and causes Barry Tilly, the other interrogator, to end up ordering him out of the room. It probably helps that Harry has seen Rudolph freak out whenever confronted with the sort of thing he deals with all the time.
Bud White from L.A. Confidential is a thuggish police officer with a penchant of assaulting woman-beaters.
- Dick Stensland is also responsible for instigating the Bloody Christmas incident by brutalizing the Mexican prisoners.

Live-Action TV

DS Jimmy Beck in Cracker, once causing his superior officer to say, "I don't know what you did to him, but you scared the hell out of me."
Sgt. Michael "Mick" Belker in Hill Street Blues, who has a habit of barking and growling like a rabid dog. And bit preps on a regular basis.
Elliot Stabler from Law & Order: Special Victims Unit, what with his desire for revenge against suspects who had abused children. Which is roughly every other week. This tendency earned him the Fan Nickname Un-Stabler. Most likely because Elliot is increasingly unstable and psychotic. That series will not end until he actually kills someone, ending his massive fall from grace. He finally leaves the police force due to his fatal shooting of Jenna Fox in the precinct. His shooting of said 14-year-old girl is justified, since she was shooting up the holding cell.
- Nate Kendall in the (ironically named) "Unstable" made Elliot look normal.
Most of the 1973 detectives in Life On Mars are unnecessarily violent by today's standards, especially in contrast to 2006 transplant Sam Tyler, but Gene Hunt deserves a special mention, here.
The retired detectives of New Tricks and their old style of policing is considered brutal when compared to modern police methods and standards. Still, they see nothing wrong with faking an act of brutality, where the interrogator gets so insanely angry that he shoots the suspect's public defender lawyer. The "lawyer" is another retired cop and the gun is a starter pistol.
- And occasionally, they find themselves working alongside an actual brutal cop, such as Frank Patterson in "The Fourth Man".
Andy Sipowicz from NYPD Blue.
Vic Mackey in The Shield has at least four excessive force complaints made against him, and hits Dr. Bernard Grady, the pedophile, with a telephone during his interrogation with him. Though usually, his menacing is done with a cold and calculating air.
Jack Regan of The Sweeney got unnecessarily violent at times, too.
Peter Boyd of Waking the Dead. A Detective Superintendent who tends to yell at the top of his voice when confronting his supsects and verges on being violent at times, though usually one of his team is watching through one-way glass and bursts in to stop him.
Jack Malone of Without a Trace is an extremely dedicated FBI agent who would do anything to get information on the missing persons case.
Several of the policemen in The Wire are rough around the edges, but standout examples are Anthony Colicchio, who attacks an elementary school teacher when said man asks him to move his car, and Eddie Walker, who out of frustration over having additional paperwork to fill out, breaks Donut's fingers over stealing a car, and causing a lot of damage to the other parked cars during the joyride.

Music

"I Shot The Sheriff" by Bob Marley. The song is about the narrator who's accused by the police of killing a deputy. However, the narrator admits to having shot Sheriff John Brown after being harassed by him (for unknown reasons) one time too many. It's also implied that the sheriff stomped over the narrator's garden while he's sowing (marijuana) seeds.

Video Games

Agent Robert Nightingale in Alan Wake is a ruthless federal agent in pursuit of the main character. Though the source for his trigger-happy behavior is explained in his backstory.
Carter Blake in Heavy Rain is an immoral police lieutenant with immunity from the local precinct (it's a miracle how) who prefers beating a suspect rather than extracting any information, has no problem with breaking the law during his investigation, and will have no qualms about arresting even an innocent person. First, he tries to scare Nathaniel Williams, a religious fanatic who wasn't involved in the murders. Then he roughs up Clarence Dupré, Ethan Mars' psychologist, who had done nothing wrong other than refusing to admit that one of his patients is a murderer. When the psychologist confesses that Ethan (who's only trying to look for Shaun, his 10-year-old-son) had visions of drowning bodies, Blake then does everything in his power to assure those affiliated with the investigation that said innocent man is the Origami Killer. The FBI agent attached to the investigation, Norman Jayden, isn't convinced, and the two have a very rough rivalry. If Ethan is arrested, then it leads to a scene where Blake will mercilessly beat Ethan into unconsciousness. Jayden can intervene and punch Blake, which will prompt him to hold Jayden at gunpoint, waiting for the perfect opportunity to kill him.
- It doesn't stop there. One of the possible endings has Blake ordering his squad of officers at the warehouse to gun down Ethan who had finally reunited with Shaun after having gone to incredible lengths to save him from drowning in the well, all while the aforementioned son watches in helplessness as his beloved father's body falls to the ground, lifeless. All because Blake refused to believe anyone but Ethan could be the Origami Killer and the instant said unarmed victim had his back turned to the police to clutches his left hip in agonizing pain instead of keeping his hands up, Blake gives the order to shoot. At this point, it's easy to say that Blake is considered as one of the most corrupt cops in fiction, even the actual villain doesn't come close to being the most disliked character in the game.
Saren Arterius of Mass Effect. As a Spectre, he's essentially a Council operative with no strings attached, due to his brutal methods in the name of keeping the galaxy safe, pursuing his own ambitions on the side and pinning the collateral damage on people he doesn't like. He's the same sadistic, racist government law officer who exists in many other works - just relocated to a sci-fi setting.

Western Animation

The titular character from the Adult Swim show Assy McGee is an extremely violent parody of brutal cops (and a Heroic Comedic Sociopath) despite being, as his name suggests, a pair of ass cheeks.
Batman: The Animated Series: Lyle Bolton from "Lock-Up" is a new chief of security who terrorizes the inmates of Arkham Asylum. He later becomes a vigilante called Lock-Up after he's fired from his position.

Real Life

There are too many instances of Truth in Television to count. It's not hard to find a list of cases where the police officers are caught red-handed using excessive force.