Whenever someone in film or on TV reports a murder, or a monster, or a stalker or whatever, the police come as close to ignoring them as procedure (and the local captain) will allow. And that's if the report is from a respected professional; if they're an Agent Mulder, or worse yet, a teenager, the cops might try to pin charges on them!
If it's a mystery with a respected Amateur Sleuth, the police detective the amateur has to deal with will be, at best, an Inspector Lestrade, and at worst an Obstructive Bureaucrat.
Also common in children's shows, since all Adults Are Useless. They might not even make it to the police station, but just (correctly) assume that no one would believe them.
In addition to police, this trope also covers the military, security guards, and other people whose job is to protect others.
A common interpretation of this trope is merely people not knowing how law enforcement actually works - This was part of why Police Quest was considered one of the most realistic games at the time it was made; because you actually couldn't just take what you thought was the obvious solution because it was either illegal, incredibly dangerous, or both. (Even law enforcement has to follow the law, despite some exceptions and what those games of cops and robbers may tell you.) Many times, the most obvious solution is actually a pretty good way to get yourself or others hurt or killed.
The Awful Truth is that this is justified - Police are more often than not, just everyday people who want to get through their jobs. It's easier to pin a crime on the guy right in front of you than to try and catch the real bad guy, who could be anywhere. In corrupt cities/states, it's even worse; law enforcement may have been bought out by a corrupt government or organized crime. Someone may cover their tracks well enough or exploit a lot of other loopholes to remain legally untouchable, e.g. Al Capone. In sparsely populated areas or small towns, chances are greater that the police aren't numerous/trained/equipped enough, but this is sometimes true of even big-city law enforcement who theoretically have to deal with a lot of stuff on a day-to-day basis. Also, the system often grades police by the amount of arrests they have made, and the amount of sentencing their arrests lead to, rather than their ability to actually catch bad guys. And, of course, some are just standard-issue bumblers. Finally, per case law, and charters and job requirements of some police departments (specifically at least the NYPD) police have no Constitutional dutyto protect citizens from harm, and some police follow this to the letter viewing their role as only to make arrests and issue fines, not to actually investigate or even save you from a criminal attack.
Some things police do in Real Life understandably seem lazy or useless to outside observers, too, when they actually aren't - like sitting in their car eatingnote As anyone who has worked any security can tell you this is a side effect of having a job where most of it is waiting for something to happen as opposed to jobs where earning money is dependent on action or a crowd of them arriving and standing around for a simple traffic stop - you can't - like a quiet day at your job - send police home just because no one is breaking the law - they still may be needed at a moment's notice!note we've all heard about instances where police officers were killed that just started out as "a normal traffic stop" - imagine how you would feel if you coworker was shot and your were sitting in your car two blocks away eating a donut.
See also The Only One and Bad Cop/Incompetent Cop, though they are not necessarily incompetent: It may just be that the "calls" are too nonsensical to be believed by someone who doesn't know they're in a show. You Have to Believe Me occurs when the police don't believe the person because the person is presenting their case in a fashion where no one reasonable would believe them. Lemming Cops is another related trope. Contrast I Fought the Law and the Law Won, as well as The Men in Black, who do believe your reports of ghosts/monsters/whatever and probably know more about them than you do, but are still bad news, and Militaries Are Useless when the authorities do try to help, but fail for dramatic tension, and The Lopsided Arm of the Law, where the police withholds its competency and firepower with little (if any) explained reason until someone tries to take the law into his own hands, and then they unleash said resources to hunt him (and only him) down.
For the complete opposite, see Police Brutality, though they can easily be combined - Bad Cop/Incompetent Cop being one example, where some cops are brutal and some are useless and some are both, and cops who are brutal but useless - as in the people they beat up and kill are innocent, while real criminals escape because they know how to play by the rules.
The AD Police from Bubblegum Crisis could save a lot of money by firing everyone except Leon and Daley. And Nene, since they'd still need a dispatcher.
Really, they just need Leon. Daley only exists to hint at Leon's closeted homosexuality, and Nene doesn't need to dispatch anyone because Leon just goes off to fight Boomers whenever. Then they could use the extra helicopter budget to fund his ridiculous revolver that can kill Boomers.
One early episode involves Ash and his friends helping a lone Officer Jenny investigate the disappearance of over a dozen children who've been missing for three days. That's right, a lone Officer Jenny who, apparently, hasn't done squat since the children vanished. (Neither have the Apathetic Citizens, for that matter, about the children or the Pokémon who've spent those three days losing energy.) Eventually, the children are found—in a public park. Where they've been for the last three days.Great work, everybody.
In another episode, the Sinnoh police are trying to stop a robbery in the Eterna museum. The stolen object in question was the Adamant Orb. However, the police force make some truly awful mistakes.
They arrest a recurring character, Nando, as a suspect, despite the fact that Officer Jenny saw the robbers (Team Rocket, naturally), of which there were two of, on the roof, who looked nothing like their arrested suspect. And this was an accusation being made by the same Officer Jenny.
When Ash and co. try to protest Nando's innocence, Jenny produces a picture of a Sunflora (a Pokemon that Nando owns, and that ran off during his arrest) making off with the Adamant Orb, and essentially declares "Ta da! All the evidence we need!", despite the fact that A: a picture like that is not enough incriminating evidence and B: anyone who would compare this picture with one of a real Sunflora could see that the one in the surveillance photo is clearly Meowth in a Sunflora costume (he didn't even bother to cover the coin on his forehead).
The police do not bother to search anyone else in the building. Lampshaded by the Jenny from Viridian City, who came to the museum because it was her day off.
In the interrogation room, Jenny refuses to listen to anything Nando says.
And finally, in one moment when Team Rocket are fleeing the building, there is a massive crowd of police there waiting for them, but due to Team Rocket being previously sprayed by a Stunky, the smell emitting from them makes all the offices block their noses and they move into what looks like a guard of honor position allowing Team Rocket to run through and escape. What. It wasn't just this idiot Jenny. In a lot of Pokémon episodes, the Jennies can't or don't do anything to stop whatever crime is happening. And quite a few times, they do more harm than good. They've let Team Aqua escape once, and on many occasions, Team Rocket.
They do seem somewhat competent whenever Butch and Cassidy are involved in something. In fact, probably the one thing that James and Jesse are better at than most other Rockets, including them, is staying out of jail.
In Real Drive, the only police presence seen are rather unintimidating, cone-shaped robots. Even when a madman runs amok in a shopping mall, mugging passbyers with impunity, no authority figure makes an effort to stop him.
In Mouse, the titular protagonist's success as a thief can be mostly attributed to the police's inability to do anything except stand around and curse his name. For instance, in the very first scene in the first episode, he steals a valuable mask by lifting the whole museum and flying it away with helicopters. The police never think of maybe following the hovering building being carried off very slowly by a large, loud vehicle? Maybe in a police helicopter? Or with a car, even? Later he also steals a tower that conveniently has a floating base by breaking its foundations and towing it out of the harbor with boats. While the police stand in the docks and marvel at Mouse's wondrous "water-traveling contraptions" that they apparently haven't figured out. Seriously, people!
The Paradigm City police on The Big O are confounded by their uselessness in the face of Humongous Mecha attacks on their beloved town; the day is generally saved by self-styled "negotiator" Roger Smith as pilot of the title mech. This is a somewhat more realistic case as trying to take down a Humongous Mecha with a measly tank just won't fly. They'd probably be pretty good at their jobs if not for that.'
The police in Lupin III sometimes come across this way, but it's more to do with who they're chasing. Inspector Zenigata, for example, is usually shown as being good at his job, it's just that Lupin is even better at his... Zenigata doesn't stand much of a chance of success, but it's strongly implied that he's the only guy who has any chance at all against Lupin.
Detroit Metal City. For all the crazy stunts Krauser pulls off in public (which includes inadvertent assault on a police officer), the police never seem to bother with following it up or taking any of the band members into custody.
The police in Code Geass are an interesting case. While never shown to explicitly kick any dogs, they are generally included in Lelouch's "all Britannian authorities are corrupt and must be obliterated" mindset. This is implied in Lelouch and Suzaku's debate in an early episode about whether the Black Knights are heroes for Justice, or whether they are vigilantes who should just join the police force and work from within the system if they want to enact change (Lelouch comments that they'd simply be absorbed and corrupted by the system). They're not shown to protect or serve the Numbers in the Ghettos, and it's implied that they may have been involved in the smuggling of Refrain. The episode in which they gain the most (and any positive) coverage is when Lelouch geasses them into shooting Mao after Lelouch beats him using that tape trick.
In the world of Hentai, at least 25% of all cases of sexual intercourse would qualify as sex offenses. And yet the only times the police can be said to be involved in the case is when a policewoman is the victim, or a policeman is the perp.
A strange example in Codename: Sailor V: the police made to look useless by Sailor V showing it up by taking not only on the youma but also on many normal criminals (the first cops to appear in the manga found that Sailor V had captured the crooks before them again). So, what does their boss do? She hires Sailor V.
In One Piece most marines are completely incapable of stopping main heroes or any other more notorious criminals running around. Straw Hats and Whitebeard Pirates seem to do a better job helping distressed citizen. However, it’s justified, because most of said criminals can turn into elemental forces at will, have Super Strength and Super Speed or are otherwise beyond ability of normal soldier to handle. Only people who can fight them are others with similar abilities (mainly other criminals like Staw Hats). Whitebeard, on the other hand, is The Dreaded whose sole name and declaration of ownership of an island is enough to keep it out of harm’s ways. This trope is also subverted by most of the marine officers, who posses superpowers or are Badass Normals themselves and proved they are more than competent when it comes to chasing down the criminals.
Perhaps the biggest aversion of this trope is the battle at Marineford. Not only do they succeed in executing Ace as planned, but when Whitebeard and his entire army shows up to stop them, they kill Whitebeard and win that fight, too. The only thing that worked against them is Whitebeard managing to spark a second age of piracy in his dying moments.
The police in Detective Conan certainly mean well, and they seem generally competent at dealing with street-level crime. But they still end up relying on a high school kid to solve every murder case in town. Most cases involve the cops missing obvious clues, which Conan has to point out to them, and then standing around dumbfounded at the end while Conan reveals the killer's identity. On the rare cases when they do make an arrest on their own, it's usually the wrong guy, and then Conan has to save the accused by finding the real culprit.
The Roanapur police in Black Lagoon are totally corrupt and impotent to the point that they can't stop crime at all, and so turn a blind eye to practically everything while taking bribes.
Meanwhile, the Japanese police aren't exactly useless and are competent, but they're pretty ineffective at dealing with the sudden rash of explosions and massacres that occur during the Tokyo arc.
Naruto: While the governments do have safety nets to deal with rogue ninjas, these are incredibly inadequate. The people in charge of taking out rogue ninjas are NamelessFaceless Goons that get slaughtered by anything stronger than a stiff breeze while said rogues are, almost without exception, THE strongest ninjas in the world.
Death Note: The Police are discouraged to chase Kira, after he killed the false L, and he forces the FBI to surrender after he killed several FBI agents. Only a few police officers try to chase him, but they are not smart enough how to do it. They need the help and lead of people who do not work for the police, but by their own. That includes the anonymous master detective L, the college student Light (who is Kira), both for the Japanese Special Unit, and the teenage L-wannabe Near for the SPK.And many states surrender to Kira.
Mello is probably Genre Savvy enough, maybe that's why he allies with the mafia instead the police.
The irony, Kira needs the police because he need names and faces of arrested criminals to kill them.
Though other members of the investigation team still manage to contribute greatly. Even the normally-useless Matsuda has some pretty big moments.
In The Lucifer and Biscuit Hammer, Nagumo quit his job as a police detective after an attempted-murderer was let off without charges being filed due to nepotism in the force. It's the last straw that leads Nagumo to conclude he's no longer able to actually help people and serve justice in the police. A later conversation with his former partner hints strongly that someone in the government is actively preventing the police from looking into the secret war, even when people die.
The police in Yozakura Quartet have their hands tied by orders from higher-up. The government, possibly influenced by the Senate, considers youkai-only problems to be hands-off. If the cops in Sakura-shinmachi want to get involved the head of the department has to decide it's gotten serious enough to warrant police involvement. What counts as "serious enough" has a pretty high threshold, though, and the one time they get orders to actively move out it's because a minor has been abducted and is about to be murdered and cannibalized, the kidnapper is also targeting one of their own, and the main characters who usually take care of everything are currently out of town. It's not even that the police can't contribute to a fight, it's that there's a lot of Fantastic Racism from their superiors who don't much care if the youkai are fighting among themselves.
Subverted in Samurai Flamenco. They're not actually useless, it's just that they tend to overlook many smaller crimes (like jaywalking and smoking in public) because it takes time from dealing with more serious crimes. The apathy is the reason protagonist Masayoshi takes up the Samurai Flamenco act. He can deal with the criminals that the police can't, or won't, deal with themselves.
Ultimately Subverted in Cats Eye: while the police seems useless at first, it's because they're dealing with the titular thieves, and we're later shown them (mostly the same cops who continue getting humiliated by Cat's Eye) proving themselves truly competent against other crooks, with the crowner being a criminal discovering the people at a coffee house egging him to confess his crimes were police officers, one of which being an old man who had earlier stolen the magazine of his gun and lured him there for arrest purpose.
City Hunter doesn't have useless cops. Their problem is that they're limited by the law and Japanese conventions, so there are things that only Ryo (who is a criminal) can do.
In Batgirl Year One, Barbara Gordon goes to a Police Ball, and they are attacked by Killer Moth. Hundreds of cops against a guy with a glue gun and less than half a dozen of thugs; and the only ones who does anything are the bibliotecary with five-inch heels and Bruce Wayne dressed as a harlequin. Police can't be more useless!
Averted in an early Captain America story when the Sentinel of Liberty is trying to stop a number of destructive Sleeper robots. He decides he can't stop them on his own and races to a military base and they take little persuasion to help the superhero fight the machines.
The Runaways' first approach to discovering their parents are supervillains is to call the cops. Alex's explanation that their parents are all supervillains does not get them much aid. Part of this may be the extent of influence their parents have. Alex is also deliberately making their story sound insane.
In Superhero comics, police officers and security guards are rarely more than an annoyance for even the lowest-level supervillain. There are occasional subversions, however, when they save the hero's life or capture the criminal before the hero does.
One such example is the Metropolis Police Department Special Crimes Unit, which was organized to oppose supervillains as best they can. More importantly, they got their own mini-series to show that they are very good at their work. Mirrored in Superman: The Animated Series where Dan Turpin saves Superman or stalls the villain long enough for Superman to catch his breath and recover. The SCU gets to fight off alien invaders while Superman prevents natural disasters they are causing, and Turpin squeezes in a Heroic Sacrifice to rescue Superman from their leader.
The Gotham City Police Department also got their own ongoing series that highlights the difficulty of being a cop in a city full of costumed whackjobs. In the first story arc, they need Batman's help to apprehend Mr. Freeze, but run down the new Firebug on their own after he murders a girl who discovers his Secret Identity. Being Gotham, especially in the early years of Batman's career, it wasn't so much "Police are Useless" as "Police are Corrupt or Too Scared To Be Useful". Perhaps best illustrated in Kingdom Come where the Metropolice PD apprehends the Joker after he's released poison gas in the Daily Planet, before Superman.
In a more general sense, this trope is averted more in Batman, where the GCPD or at least Gordon and co are important allies of the Bat, than it is in most superhero comics where it's played straight.
Another subversion occurred as far back as the 1960s in an early Spider-Man comic, where Spider-Man tracked down the crime boss known as the Big Man and captured most of his gang for the police but the Big Man gets away. Thinking that the Big Man is his boss, J. Jonah Jameson, Peter Parker returns to the Daily Bugle in hopes of helping the police catch him. It turns out, though, that Peter was wrong, and the police managed to track down the real Big Man, who was in fact reporter Frederick Foswell.
Averted in Starman. The O'Dares, a family of policemen (and woman), regularly help Jack because his father saved their father. They start by capturing the Mist while Jack fights the Mist's son and keep up that track record throughout the series. Jack & his father consider them friends and celebrate Christmas with them.
Elks Run looks like a case of this at first, and the initial two policemen sent to investigate don't survive very long. However, it's a major plot point that Conservation of Ninjutsu does not apply to the cops—if reinforcements come, everything's over.
Averted in Judge Dredd, the Judges are the only ones capable of reigning in the anarchy of the future because of their extensive training and military hardware, they're so heavily armed that they even have tactical nukes at their disposal in case of an invasion. Taking on a Megacity with anything less than an decked-out army of millions is suicide.
Powers is about averting, subverting, playing straight, and generally deconstructing and reconstructing this trope in a world of supers. Powered people aren't allowed to be cops, and the main characters work in a super-homicide department trying to catch and police people who can kill other supers. They're fairly effective most of the time, but other times they get completely stonewalled by politics, lawyers, most supers' celebrity and wealth, and the general difficulty of figuring out means, motive, and opportunity when powers and larger-than-life personalities come into play. If an actual fight breaks out they're often in trouble without a friendly super anywhere nearby.
Half-Life: Full Life Consequences: Not only does the only cop to appear try to give John Freeman a ticket for speeding (when he is trying to rescue Gordon Freeman), but he is headcrab zombie as well!
legolas by laura: Technically they're not police, but the guards - sorry, ''gards'' - assigned to protect Laura are thoroughly useless. The orcs sent to kidnap Laura get in, get out and get all the way back to Mordor before they tell Legolas that Laura was taken. Even then, Legolas had to ask first.
The basis of Lance Manley's possibly true memoir Stab Proof Scarecrows: about his (short) time in the English police. It shows an organisation obsessed with looking good at the expense of public safety with Race & Diversity the focus of attention rather than actually solving crime.
Part and parcel of the Nancy Drew and The Hardy Boys books, since having a competent police force would render the need for crime solving eighteen-year-olds unnecessary. The same goes for Trixie Belden.
In Tamora Pierce's Provost's Dog novels, this seems to be the case for Night Watch and any of the Dogs portrayed unsympathetically. Taken up a notch with Sir Lionel of Trebond, which causes this trope in the Port Caynn Guard by extention—he's not only incompetent, he's an incredible coward willing to put up with huge amounts of criminal activity to save his skin.
Even the Evening Watch, which is depicted as the best of the bunch, is limited, as much as they loathe to admit it. They're understaffed, underfunded, and have to put up with an unfortunately high level of laziness, corruption and brutality because of it. The well meaning cops do their best, but sometimes that's not enough.
Averted with the Special Investigations unit in The Dresden Files, led by Karrin Murphy, who among other things has taken down a tree-monster with a chainsaw. Though the unit still calls in Dresden for consulting, it's mentioned a few books in that they've learned enough to handle most of your usual supernatural riff-raff without the wizard's help. There are also things with enough power that getting the police involved would lead to a bloodbath. Several times Dresden convinces Murphy not to involve her unit by telling her what he's facing is "worse than the loup-garou", a Nigh Invulnerable variety of werewolf that rampaged through the station in the second book.
In the early Sherlock Holmes stories, the police inspectors of Scotland Yard were outright idiots, overlooking clues and coming to false conclusions. In The Sign of Four Holmes proclaims, "I would rather have the help of Toby (a dog) than the entire detective force of London!" This was improved in later stories, as Inspector Lestrade, especially, was shown to be more lacking in the specialized knowledge and Hyper Awareness that Holmes possessed, than simply being a moron. Holmes even praised Lestrade and Gregson for their courage and tenacity, even if their own detective skills were lacking by comparison.
This was in response to the development of forensic science; when Doyle started writing the stories, the police often failed to take statements from witnesses at crime scenes. As time passed and investigation improved, so did their treatment in the stories. Holmes was always better than them.
Indeed, it's said that the real Scotland Yard detectives read Holmes novels, and took hints. It's worth noting that many things that Holmes does that are common police procedure today were barely given a lip service in the 19th century.
Even leaving aside the lack of development in forensic science, at the time Doyle started writing the Metropolitan Police had developed a reputation for being woefully incompetent and corrupt. It was also around this time that the Jack the Ripper murders occurred, and it soon became apparent that the police were completely ill-equipped to deal with what was going on; as a result of this, serious and long-needed reforms began to be introduced.
Even the ones with the Order are still incompetent, except for Moody. Tonks loses every fight she's in. No Auror can handle Bellatrix Lestrange... who is beaten by a housewife. Another Auror loses in battle with Neville's grandmother. It would seem McGonagall was fibbing when she told Harry about the high standards just to qualify for training for the Aurors in an effort to trick him into focusing more on his studies.
In the Montmorency series, especially the fourth book, the police do very little to help, including capturing the wrong person on a few occasions. But they try. Really, they do.
The City Watch in the Discworld novels started out in Guards! Guards! as basically an intentional parody of itself; the Thieves' Guild was better at regulating crime, for one, and eventually the watches were filled up by Vetinari with useless no-hopers, led by an alcoholic Sam Vimes on nights. Then events happened, propelling things to the current status.
Cops tend to be fairly useless in Stephen King's books. Even when they're persuaded to investigate the strange goings-on in a particular novel, they have a tendency to get bumped off before they can help the heroes.
There's a BIG exception on Needful Things, though; the main character, a small-town sheriff, manages to single-handedly fight off a demonic Puppet Master. Most of his deputies manage to handle themselves half-decently considering the circumstances, too.
In Very Bad Deaths, Russell is hunting Alan, a serial torturer/killer, from information gleaned by his telepathic friend's brief brush with Alan's mind. When Russell gets a police officer to listen to him, she can only help him as a civilian because the police can't legally act on any of the (scant) information he has on the Alan.
The police in Incompetence, as the book's title suggests, are completely useless. Examples include an officer suffering from "Non-Specific Stupidity" who manages to handcuff himself while arresting a suspect, a food safety officer who brings SWAT teams on restaurant inspections and a police captain with anger management problems so severe that he opens fire at the pavement when told to calm down. The one police officer shown to display any form of competence is said to have zero promotion prospects due to this fact.
In Goose Girl, Ani/Isi is snatched off the streets during the festival and the King's Soldiers, who are there, don't do squat. Later she points this out:
"Did you know that there are men who call themselves Peace-Keepers, obeying their own code of law and not the King's, sworn to keep the streets safe because the King's soldiers do not, or will not?"
In The Inkworld Trilogy, Meggie and her aunt go to the police, but the police refuse to come. Also subverted, when one of the police turns out to be employed by the Big Bad. Precisely one cop, who is able to hide the illegal activities of a town, which include regularly kidnapping people.
In the Children of the Red King series, the police appear occasionally, but there's not really anything they can do about say, a murder committed by a 300 year old magically animated sword. Generally, they just ignore it and hope the endowed people can solve their own problems.
A military variant happens in The Destroyer #113, "The Empire Dreams". The neo-nazi villains successfully blitzes London three times because the same obstructive RAF officer keeps refusing to take the reports seriously. The first time he rejects the reports because they were made by a farmer and a meteorologist and who would fly WW2-era planes anyway? He later rejects a second report because it says the planes come from the direction of the English Channel, and the first planes obviously came from Ireland. In the third case they actually have a tight security net up, but fail to consider planes launched from within Britain, so he rejects those claims too, because "nothing can get through our security measures". He then accuses the near-hysterical official reporting the bombings of being drunk, while gunshots, explosions and screams can be heard in the background. The villains later seize Paris by kidnapping roughly over a dozen important officials, including the French President, and torturing them until they sign a surrender. The entire coup is carried out one morning without any mention of interference from bodyguards or police, and the new regime has their jackbooted neo-nazi skinhead troops marching in the streets the same day, with no visible resistance at all.
Amelia Peabody and her husband, who are detective archeologists, routinely ignore the police in their detective work. Justified, in that their adventures happen in Egypt in the 1880s to 1920s, where the police are indeed ineffectual, violent and corrupt. Things get better by the end of the series, but by then, their habits are ingrained, to the chagrin of the new police inspector.
In Death series: Played with. Averted with Eve Dallas, who is a cop and the best officer to go to if there's a problem. Played straight with other police groups, because they are inexperienced, incompetent, lazy, insensitive, too stubborn, too territorial, have a lack of instincts, out for glory, dirty cops, and so on. Fortunately, Eve's squad has closed a number of cases, which shows that Eve is not the only effective cop out there.
A variant occurs in Animorphs, where going to the police or even sometimes the army is out of the question because a percentage of the force are controllers and going to either cover up whatever it was to keep the invasion secret or just turn in the Animorphs or both. It's hard to tell who's a controller and who isn't.
Sisterhood Series by Fern Michaels: Played very straight! The cops know who killed Barbara Rutledge in a hit-and-run in Weekend Warriors, but can't do anything about it because the driver uses Diplomatic Impunity. Indeed, the Vigilantes operate under this assumption, and considering how the police are often incompetent or in the bad guy's pockets, that assumption may not be too far off!
Enid Blyton's popular Famous Five series has the Big Bads committing heinous acts and the police completely unable to find even the smallest piece of evidence against them. In the end, the police are the ones who arrest the Big Bad, but it is a certain group of teenagers and a dog who find all the clues and figure it all out.
The NYC police in Psmith, Journalist don't take any of the gangsters seriously, even when they're out to kill the main characters. Even if taken into custody, the gangsters can always provide each other with alibis and get themselves released.
In Neil Gaiman's Coraline, the titular character calls the police after her parents disappear without a trace. While she explains herself in terms that may sound like a child having a nightmare, it's still no laughing matter when she tells how her Other Mother probably made them disappear; rather than brush her off, it would seem more likely for the modern police to interpret what happened as murder or kidnapping over custody disagreement.
In the Ancient Egyptian mystery novel Eater of Souls, a serial killer's initial crimes go unsolved — indeed, virtually unnoticed — because the head of the city's police force is a lazy status-seeker who writes the victims off as "A death, not of the city", simply because he doesn't think his superiors in the nobility would want to be troubled about something as sordid as murder among visiting merchants or villagers.
After Honor Harrington is attacked by a crewmember who tries to assassinate her, she instantly deduces that he was under some kind of mind control, which the military police brush off as denial that someone she knew was an enemy agent.
This, however, isn't shown to be the norm, but simply a narrow-mindedness, rather than genuine incompetence, of the investigator in question. Overall, most police services in the Honorverse are shown to be quite competent, and even when corrupt, they at least aren't completely bumbling in their corruption.
Also, Honor didn't deduce anything, she knew that Lt. Mears was under some sort of influence, because of her empathic sense. Which she had to present as being that of her treecat, to keep The Masquerade. The investigator simply didn't believe in the 'cats Psychic Powers, because at that time they were more of a hypothesis rather than an established fact, and were dismissed even by many respectable scientists.
In the children's book Corduroy, the night security guard takes a stuffed bear as a perfectly logical explanation for the crash he heard. He puts Corduroy back on his shelf and does no further investigation into the incident.
Detective Lieutenant Willer and his entire force in Tyrannosaur Canyon are dismal at every point of the story. They allow the scene of a murder to degrade for several days before following up, blame the protagonist for everything, and are cowed into submission by the feds right before they could have been useful.
In WHO dunnit, a high-profile murder at a prominent hotel-casino doesn't warrant any attention from the police. It's up to the player's Hardboiled Detective to solve the case.
Generally averted in Adventures in Odyssey, where most of the police are played straight and do their jobs just fine — sometimes in detail. However, there was one notable exception early in the show: Officer David Harley, an absent-minded, bumbling police officer who was a recurring character and ready-to-go comic relief. However, he was pulled off of the show when parents complained that he was presenting the wrong image of police to kids.
The radio play Sorry, Wrong Number is about a bedridden woman who overhears on the phone, in detail, a conspiracy to commit murder. When she calls the police, they aren't really interested in looking into it.
Given how prevalent the military version is in Zombie Apocalypse fiction, it's worth noting that it's averted in Unhallowed Metropolis. The main deciding factor in whether a country or region still exists is whether or not there was a swift and effective military response, whether it consisted of actual military strikes to curtail the Animates, erecting fortifications, or simply fleeing to more defensible geography.
Depending on the GM, it can happen and be justified in the d20 Modern Urban Arcana setting, by the fact that the police/army are not being properly trained/equipped against supernatural threats. (Even highly trained Navy Seals will have a hard time bypassing a lycanthrope Damage Reduction 15/Silver without, well, Silver Bullet, which are not standard issued in any military force.)
Averted and played straight in Warhammer 40,000, on the ground level, most Imperial Nobles have all sorts of law enforcement; from Enforcers, to Guard, to Police, all of which are usually not much better than a gang of ugly theif takers who simply enforce the will of the ruling Noble. The ubiquitous police force used by the Imperal Government proper, however, are the Arbites. These guys carry more guns and heavier armour than SWAT teams, tend to be fanatics who have borderline worship of the law, and have a habit of beating most unimportant suspects to death. Might have something to do with the fact that the Adeptus Arbites is a giant Shout-Out to Judge Dredd.
World of Darkness has shades of this, and sometimes jumps headlong into it. While it can be justified, there are other times that are extremely questionable.
One flavour short story involved a pair of cops practically wetting themselves after firing at a man who was drinking blood from a corpse. Since - to the reader - it's obvious the man was a vampire, it appears justified, but the police officers - having fired only at his torso - had no reason to believe it wasn't a regular guy in a bulletproof vest (probably on drugs, too), it really makes these cops seem particularly incompetent.
Played for Laughs in Arsenic and Old Lace, where the beat cops who visit the Brewster house to pay their respects to the protagonist Mortimer's sweet old aunts remain cheerfully oblivious to: (a) the mysterious disappearance over the past several years of a dozen old men who've entered the residence; (b) the sudden appearance of a highly wanted Serial Killer; (c) the fact that Mortimer is tied to a chair involuntarily and is about to be tortured to death by said serial killer; (d) the presence of said killer's equally wanted accomplice in the same room even after the killer himself has been recognized and captured. By contrast, the one time they do act rationally is the one time that Mortimer wishes that they wouldn't: when his sweet old aunts innocently confess to the murders they've committed right in front of the police captain.
In RasputinCatamite, The local police seems lazy, adverse to paperwork, hideously bigoted and corrupt.
In Shortpacked!, Ethan calls 911 after his Roadblock poster and Roadblock action figure start sexually harassing him. He gets hung up on almost immediately, as you might expect.
The Inexplicable Adventures of Bob! has two local cops named Baskin and Robbin (as opposed to the two recurring federal agents, Ben and Jerry) who diligently ignore all the seemingly nonsensical "crank calls" they keep getting about flying saucers, unicorns, dragons, robots, and the like. Like so.
Daisy: This isn't like [dad] at all. We need to go find him. Cooper: Shouldn't we call the police? Daisy: Yeah, sure. And then we can have ice cream with a nice lady from the DSS. And she'll ask us why Daddy's not home, and why he's an owl, and why he doesn't wear pants, and so on.
In Sluggy Freelance the two-man police force in Podunkton actively discourages people from reporting crimes. Deputy Edsel is a straight example, whose first response in the face of an emergency is to say, "Somebody should call the police!" Officer Tod, however, is actually quite skilled, but he prefers to just let Oasis chop criminals into little pieces, while he gets paid for doing absolutely nothing.
When Zoë tries to tell some apparently less dishonest policemen that she was kidnapped into a building that turned into a rampaging ground for "zombgeeks" (don't ask), she runs into a downright parodic version of the trope. Sure, her story is extremely implausible, but the policemen are also ignoring the fact that when they went to check it out, "a rocketship made of mucus and unidentifiable bits burst through the roof." Apparently they thought this wasn't anything unexpected because "it's a Monday."
In the Web Comic''Zeera the Space Pirate,'' Zeera at one point tries to go straight and joins the space cops, only to discover that the space police are so corrupt that piracy was actually a more honest career choice, and she reverts to being a pirate. Since then, she has met a few cops who are honest and are trying to reform the organization.
Suicide for Hire; the cops never seem to get anywhere. A rash of gruesome teen deaths goes unheralded by the news and not investigated in any detail, and acts of violence in public go ignored, such as when Autumn pulls a knife and attacks another girl at the prom. They did respond and do their best to deal with a case of domestic violence (the author of the comic has been trained to work with victims of domestic violence and didn't want to make light of it) but the victim's non-compliance meant they couldn't convict the attacker.
Ansem Retort: the police have been muzzled by a state law that all crimes committed by people on TV are ignored to protect the entertainment business. Notably, the closest Axel came to being actually punished for his many, many crimes against humanity was before he was on TV.
In Mayonaka Densha whenever the police show up they only serve to make the situation worse or just don't do anything at all. Then again, they are being lead by the man himself, Inspector Lestrade.
Every example of the police in Drugs And Kisses, much to the delight of the main characters
Survival of the Fittest has the Denton police force, who are either too corrupt or too incompetent to deal with any of the gang violence rife in the city. This is to the point where the gangs practically run the place, shootouts and mass brawls being a common occurrence.
Bee and Puppycat: While Bee is waiting to cross the street, two police in a cop car drives to the intersection and stops to glare at her to make sure she doesn't jaywalk while ignoring two kids running across the street to chase a duck.