The room is small. Help is far away, on the other side of many locked doors. Your arm is chained to the table and a Rabid Cop is spraying spittle into your face in a way that convinces you that he has completely lost his mind.
All he wants you to do is admit that everything Hitler did was your idea. Sounds good to you. What do you have to sign to get away from this maniac?
The Rabid Cop might be casually dirty, or overbearingly self-righteous, or anywhere in between, but they all have two things in common: a reckless 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 it. Likely to enjoy using Torture for Fun and Information.
Compare/contrast the (presumed) sympathetic Cowboy Cop.
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Although he isn't in the circumstance described above, Alonzo Harris from the film Training Day is the embodiment of this trope. He is not necessarily insane though, just genuinely evil and sociopathic.
Dennis Peck from Internal Affairs ...see Alonzo.
Agent David Kujan pulls this on Verbal Kint a couple of times in The Usual Suspects. ("I've got immunity now." "NOT FROM ME! There IS no immunity from me, you piece of shit!")
Officer Mooney in Killer Klowns from Outer Space has to be almost physically restrained from beating up a couple of punks brought in for public drunkenness. He later takes a flashlight to the head of one of the klowns, which turns out to be not such a hot idea.
In the first Saw movie. David Tapp's recklessness nearly kills one of Jigsaw's victims, gets his partner shot by multiple shotguns at once, gets his own throat cut, nearly killing him, and gets him dismissed from the force. And that is just backstory. By the time the events in the movie proper start, he is a broken shell of a man in a fetid bedsit across from the house of the guy he thinks is the killer. It is arguably creepier than any of Jigsaw's actual traps.
Detective Eric Matthews in the second movie. As the movie progresses, it's revealed that he has a very nasty record of violence towards suspects, and in several cases planted evidence to gain a conviction. And after spending most of the film watching his son trapped in a house with the victims of said evidence-planting, he resorts to thrashing the living daylights out of Jigsaw for the location of the house, which turns out to be a trap set up specifically for Matthews.
Live Action TV
As illustrated above, Andy Sipowicz from NYPD Blue.
Before Andy Sipowicz, there was Mick Belker on Hill Street Blues. Dude even barked and growled like a rabid dog. Bit people on a regular basis. "You gonna tell me what I want to know or am I gonna have to show you my ass!"
Law & Order: Special Victims Unit's Elliot Stabler can cross into Rabid Cop territory, especially when It's Personal. 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 mot end until he actually kills someone, ending his massive fall from grace.
The cop in the (ironically named) episode, "Unstable", made Elliot look normal.
Most of the 1973 detectives in Life On Mars are rabid by today's standards, especially in contrast to 2006 transplant Sam, but Gene Hunt deserves a special mention, here.
Most of The Shield features the police mavericks trying to escape the consequences of doing their jobs this way. Vic Mackey in particular counts as such. While he is a proponent of the Jack Bauer Interrogation Technique, Vic only rarely turns into the rabid cop - usually, his menacing is done with a cold and calculating air.
Peter Boyd of Waking the Dead tends to get EXTREMELY SHOUTY and verges on 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 can be pretty worked up and he will do anything to get information on on those poor missing people.
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.'
Several police on The Wire, but standout examples are Anthony Colicchio, who attacks a middle-school teacher for asking him to move his police car, and Eddie Walker, who breaks a teenaged carjacker's fingers just for giving him additional paperwork.
The retired detectives of New Tricks have slightly Cowboy Cop attitudes compared to modern police methods and standards. So they see nothing wrong with creating a fake Rabid Cop scenario 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.
The aptly named Detective Slaughter from Castle, a one episode character played by Adam Baldwin.
Ray has moments like this in Breakout Kings, including threatening to burn a suspect's genitals with a cigarette lighter.
THAT! IS! NOT! MY! COW!. Vimes does whatever he can not to turn into one, to the point that he actually has a Vimes-esque entity in his mind to prevent him from succumb to the darkness.
"Who watches the watchman? I do."
Averted in The Dresden Files book Changes. Rudolph tries his best to play the Rabid Cop, but all his desk-pounding and spittle-flecked screaming manages to do is cause Harry to crack up and the other interrogator ends 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.
Captain Zuccho from Incompetence has a Hair-Trigger Temper, to put it lightly. Asking him to calm down will result in him randomly shooting at the pavement. Reputedly, he is on Prozac, but it doesn't seem to be helping.
Lt. Carter Blake in Heavy Rain is a police officer with immunity from the local precinct (why, nobody knows) who prefers beating a suspect rather than extracting any information, has no problem with breaking the law in order to investigate, and will have no qualms about killing. Initially, he's rather reserved to just beating suspects, and then he roughs up a psychologist who has done absolutely nothing. And then does everything in his power to assure those affiliated with the investigation that Ethan Mars 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 possibility at the end of the game has Blake order a sniper squad to gun down Ethan who had finally reunited with his ten-year-old son after having gone to incredible lengths to save him from a horrible death, all while the aforementioned son watches in horror 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 the obviously unarmed Ethan has to clutch his side in pain instead of keeping his hands up, Blake gives the order to shoot. Needless to say, Blake is by far the most hated character in the game, even the actual killer doesn't come close. The worst part? In any good ending he gets away with everything.
Saren Arterius of Mass Effect. As a Spectre, he's essentially a Council space cop with no strings attached, and he plays it to the hilt - making frequent usage of the Jack Bauer Interrogation Technique, 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 we've seen in many other works - just relocated to a sci-fi setting. And this was what he was like before he went Jumping Off the Slippery Slope.
Agent Nightingale in Alan Wake really fits in this trope. Though the source for his jerkassery is found in his back story.
A good way to lose in Police Quest, acting like the aforementioned Carter Blake above will not be tolerated in the force.
This is parodied in The Boondocks where a Rabid Cop violently accuses and assaults Butt Monkey Tom Debuoir for a crime that he obviously didn't commit before being forced out by the nice cop. He then rushed in 5 seconds later to assault Tom again.
The titular character from the [adult swim] show Assy Mc Gee is an extremely violent parody of this trope (and a Heroic Comedic Sociopath) despite being, as his name suggests, a pair of ass cheeks. He was perpetually intoxicated, told to hand in his badge and gun at least once an episode, and other offenses too numerous to list here.
Iron Man Armored Adventures gives us their take on the NYCPD and the inexplicability of Family Friendly Firearms at the same time. Doppelganger!Tony has just shot at unarmed people at a party with a laser gun and rushed off. The real Tony Stark is taken in for questioning, and one of the officers is like this, complete with banging on the table and yelling, "Did your friends give you the lasers?!"