"And to his left is your typical drunken, oafish police chief with his hat on crooked, most likely named Barney O’Blarney or Patrick O’Hallorahanfitzmichael or something like that."
In every police precinct, you'll have several stereotypical types of cops. The most common of these will always be the O'Hara, the cop with the whimsical Irish accent who usually stands in the sidelines, offering recycled stereotypical quips about St. Patrick and the shores of Oireland.
Truth in Television, as in New York, Boston and Chicago Irishmen were disproportionately represented in the police- massively. (This is the reason they called it the "Paddy Wagon", and why "shamus" (Séamas) became slang for detective.) Around 1900, five-sixths of the NYPD was Irish. A large wave of Irish immigrants in the 19th century coincided with the time when major cities started establishing "professional" police forces, and police work was one of the few jobs open to Irish immigrants at the time. In Real Life, police forces offer many opportunities for recent immigrants, and they sign up, partly to protect their own people. Because early police work closely resembled thuggery, it was not a prestigious position, and because poorly paid police were vulnerable to corruption, the police were widely despised. It did not take long for the urban police and The Irish Mob to become partners.
Mostly a Discredited Trope these days. Of course, Irish-American cops still show up frequently (noticeably in The Departed in which nearly all the cop characters are Boston Irish—and all of the criminals are part of The Irish Mob), but the just-off-the-boat accent and whimsy are long gone — except somewhat in Historical Fiction. In modern works, Irish-American officers might be following in the footstepsof several generations of police families and/or trying to live up to a parent who died in the line of duty.
Compare Irish Priest, the other stereotypically Irish profession in American fiction.
Examples:
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Advertising
Officer Clancy in this vintage Australian ad for Fanta.
Anime
The first American dub of Rurouni Kenshin had the cops sporting Irish accents; fortunately this tested so poorly that it went back for redubbing before the commercial release.
Patlabor fell into this trope more or less by accident (there is no evidence they did the research), by giving their (half) Japanese-American New York Cop the very Irish (and noted) name of Clancy, Kanuka Clancy (a Shout Out to Tom Clancy). It helped a lot of fans with the Fridge Logic of why someone from Hawaii would join the NYPD.
Comic Books
Comics where Mickey Mouse is a detective (often Mickey's on-again, off-again freelance job) have a beefy uniformed police chief named O'Hara as Mickey's boss. He originally appeared with an accent, though in the 1960s it was dropped. In a few later cartoons (notably on House of Mouse), O'Hara did appear with an accent. And it's back, too, in most new comics produced since the 1990s. It must be noted that with or without the accent, Mickey's O'Hara is a competent, long-suffering cop whose real problem isn't his own weakness — it's that his chief of detectives, Mr. Casey, is an overconfident blunderer (whom Mickey has inadvertently upstaged many times, leading to a friendly rivalry).
Chief O'Reilly from the Bananaman comic book and animated series, who was a parody/homage of Chief O'Hara from Batman.
Averted in the Starman comics with the O'Dare family of Badass Normal policemen and women.
It is only averted because the O'Dare family are actually third generation, though Kate, the only female of the group whom is a cop, acts in a very stereotypical Irish spitfire way.
X-Men Noir is set in 1937, and Chief Eric Magnus is an Eastern European immigrant cop who is bitter over being discriminated against by the Irish-American cops who dominate the NYPD; he claims he failed the Sergeant's Exam three times just because he doesn't have a shred of Irish heritage. It's never explicitly spelled out, but it's notable that none of the members of his clandestine "Brotherhood" are Irish, either.
In Spirou's Luna fatale, all NYC policemen have irish names.
Film
Bridesmaids provides an unusual recent example with Officer Rhodes, although to be fair, he's not very Oirish outside of the accent.
Sean Connery's character in The Untouchables, who was completely and utterly invented for the movie. In real life, Eliot Ness knew what he was doing from the start, and didn't need a wise mentor to show him the ropes, but apparently that wouldn't be dramatic enough. Also, Sean Connery is not Irish, no matter what the other characters say.
Irish cops aplenty in the movie Blown Away, set in present-day Boston. To judge from this movie, it seems that the Boston Police Department recruits solely from those fresh of the potato boat from Ireland.
All the cops in The Boondock Saints are Irish descended (with a touch of an accent) with the exception of Smecker, the only officer/agent from outside Boston.
None of the police officers in The Boondock Saints have Irish accents; they just have Boston accents. And they're not all Irish-descended, either: Detective Dollypoposkallius is very much not Irish.
Hoodlum provides an example with Captain Foley's character. Crooked type.
In L.A. Confidential, James Cromwell's police Captain is this complete with the off-the-boat accent.
Even using the boyo thing.
Subverted in Super Troopers; Captain John O'Hagan of the Vermont State Police is probably the most competent and serious member of his department. In fact, he's probably the most competent and serious officer in the whole movie. He also takes a moment to mock the trope by briefly adopting a brogue and saying the following line when one of his men is trying to pull a fast one on him:
I'll believe ya when me shit turns purple and smells like rainbow sherbet.
Officer Mulroney (the ultra-Irish looking John C. Reilly) in Gangs of New York is a former Irish gang member who fought with an axe. He now works for Nativist gang leader Bill "The Butcher" of the Bowery Boys.
Mulroney: (as he tries to kill Vallon) Ach, do ye remember yer fadda, lad. Ooh, the toimes we had...
Barry Fitzgerald plays one of these in the old noir flick, The Naked City. And he is awesome.
Played for gags in the 2005 version of The Producers (which is set in 1958, when this trope had already become irrelevant in Real Life). Two NYPD cops with very thick stereotypical Irish brogues come to investigate goings-ons in Max Byalistock's apartment and discover Max and Leo Bloom's "cooked books" from their fraud scheme. Also, Max Byalistock (Nathan Lane) tries to bluff his way past the cops by assuming a ridiculous parody of a brogue in which his voice keeps getting higher and higher.
In the 1978 Superman, the first two Metropolis police officers to encounter the Man of Steel are straight examples of this trope.
Parodied in The Other Guys during the scene in the Irish bar.
Several Irish-American policemen and other civil servants appear in the John Ford film The Last Hurrah, most notably at Knocko Minihan's wake, when the Irish-surnamed officer assures Mayor Frank Skeffington that "The whole precinct is behind you".
In the Disney made-for-TV movie Michael O'Hara the Fourth, the first Michael O'Hara was a typical Officer O'Hara and since then there has always been an Mochael O'Hara in the police force (although the later ones were not noticably Irish).
Stephen King featured an Irish cop in It, down to the Batmanesque "Chief O'Hara" accent. One of Richie's funny voices in the same story is also the Irish Cop.
Officer Nell shows up in other King stories set in that area, too.
There's a scene in The Haunter of the Dark where the protagonist is researching a local desecrated chapel, and is told that all the Catholics in the area know the story behind it. So he asks the nearest police officer, "a great wholesome Irishman."
Captain Dudley Smith may seem like this in James Ellroy's L.A. Quartet but is in reality something very different.
Roald Dahl wrote a short story in which a wealthy New York couple, having forgotten their keys, attempt to break into their own house - and are promptly shot dead by a gang of Irish cops.
The Cabinet Of Curiosities features NYPD officer Patrick "Paddy" O'Shaughnessey, who is described as having "probably the most Irish name in New York." The book then goes on to subvert the trope at every turn, making him a boon to the investigation, a guy with a standard New York accent, and a lover of opera.
Invoked in Tom Clancy's Patriot Games when Jack Ryan tells the Queen that Irish Americans have a tradition of being the forces of order — cops, firefighters, and clergy, especially — and nowadays, the most famous Irish in the world are terrorists, something Jack is certain his father, Officer Ryan, wouldn't have liked at all. "He spent his whole working life taking animals like that off the street and putting them in cages where they belong."
Julius Cohan in Tales from Gavagan's Bar.
From the Harold Shea series (by the same authors), there's Pete Brodsky, a.k.a. "the synthetic harp".
The Betsy series by Carolyn Haywood features a friendly red-headed policeman named Mr. Kilpatrick. At one point he talks about his granny in Ireland.
Karrin Murphy of The Dresden Files is a Chicago cop, a member of a large clan of cops and has a very Irish surname.
The Past Doctor Adventures novel Illegal Alien, which transposes a number of American hardboiled detective tropes to Britain, plays with it by having a Northern Irish Chief Inspector in the Met, who says things like "Saints preserve us", but also suspects all Irish-Americans of being IRA sympathisers.
Live Action TV
9/11: The Tearjerker finale of this documentary showed a picture of each of the fire and policemen who died in the Twin Towers. The musical accompaniment was "Danny Boy," which fit because an enormous amount of them were Irish.
Batman: The 1960's show probably has one of the more famous O'Haras, named O'Hara.
O'Hara also appeared in the comics, first mentioned slightly after the show's debut, but not actually appearing on-panel until well into the 1970s. He has appeared sporadically in later years, though usually not as part of the main Batman continuity.
One episode had five cops named O'Hara, O'Malley, Douglas, O'Reilly, and Goldstein.
Blue Bloods: The Reagan family is of Irish descent (the new mayor even calls Frank a "white Irish cop" in the Season 2 premiere), but the trope is averted quite handily.
Castle: Downplayed Trope with Kevin Ryan. He doesn't have the accent and is at least one generation, possibly more, removed from Ireland. Still, references to his Irish heritage crop up now and again, such as being Raised Catholic and having gone undercover with an Irish-American gang in his earlier years.
Copper: Justified Trope since it takes place in 1864. The rank-and-file police officers shown are first generation immigrants who were born in Ireland. The police officer protagonists are named Corcoran, Maguire and O'Brien. Corcoran even lampshades the fact that their captain is as Irish as they are but the captain's father dropped the 'O' from O'Sullivan when they arrived in America.
CSI NY: Averted Trope. Mac is at least half Irish, and Flack is probably Irish, but they don't fall into the trope.
Harry And Paul: Sent up with Officers O'Malley-Mulligan-Hoolagey and O'Pat-Eddery-Flannery-Hoonigan in "The Cops" sketch:
Law & Order: Detectives Greevey and Logan from season 1 are both Irish-American, as is ADA Stone (and later Jack McCoy). Inevitably, there's an episode involving The Troubles.
And Logan's Law & Order: UK expy, Matt Devlin, though it never becomes an issue, except in one scene where he references his heritage in order to gain the trust of a young prostitute he's questioning, and another where he mentions being hassled about it during his rookie years, "I was called "mick" for the first six months because my family's Irish". Oddly enough, despite the UK setting, this is about as close as a reference to The Troubles as we've gotten.
Murder, She Wrote: There was at least one episode with a police Lieutenant with the typical Oirish accent with all the stock phrases. And another set in Oireland with the local cops that way.
Directly addressed in a skit at the end of the Indestructible Man episode. After Joel swears to stop making jokes about policemen and their alleged love for doughnuts, Kevin Murphy and Mike Nelson appear as policemen and begin complaining about other stereotypes about the police, including this one.
Ohara: This short-lived 1980s cop show played with this trope — "Ohara" (without an apostrophe) is a Japanese name, and the title character, Police Chief Ohara, was played by Pat Morita.
Psych: Averted Trope. There is an Officer O'Hara, but that's her name. Her partner, Lassiter, is Irish, but he doesn't act like this and isn't native to Ireland.
It doesn't help that Lassiter's actor once played an evil leprechaun in a Disney film.
Revolution: The O'Hallorans, the neighboring family that is burning Drexler's poppy fields, are a long line of such, although the father's primary motivation is personal—Drexler killed his daughter with a heroin overdose.
Single Handed: This is an Irish show about an Irish Garda in Western Ireland.
The Wire: Notably Averted Trope, which acknowledges the Irish influence on the Baltimore PD - the main character McNulty is Irish and a drunk, but a highly competent detective, and there is a tradition when a cop dies of holding a rowdy wake to The Pogues' "Body of an American" - but doesn't have any comedy accents.
In particular, while some Black officers will make jocular remarks about the changing nature of the racial makeup in the Baltimore PD, the influence of an Irish background doesn't seem to go past a family name and possibly being Catholic. Prosecutor Rhonda Perlman even remarks to a hungover McNulty that being a drunk Irish-man he's useless, (read: momentarily impotent) but then again he's not really Irish.
Music
Also regarding The Pogues is their hit Christmas song "Fairytale of New York", whose chorus goes "The boys in the NYPD choir were singing "Galway Bay" // And the bells were ringin' out for Christmas Day."
Billy Joel's Movin' Out (Anthony's Song) namechecks a certain 'Sergeant O'Leary'.
From all the way back in 1896, Percy French's The Mountains of Mourne has a verse in which the singer (an Irishman gone to London to seek work) encounters his old friend Peter O'Loughlin who is now "the head of the force".
Radio
Officer O'Ryan fit the trope to a T in Adventures in Odyssey, in fact he was the town's only cop until the introduction of Captain Quinn.
Invoked in The Jack Benny Program whenever they did a mystery sketch: Jack played "that master super-sleuth, Captain O'Benny", and other characters playing his assistants got O's added to their names too: O'Harris, O'Day, O'Wilson... Although when Dennis Day tried to ham up the role with an Irish accent, Jack told him to "cut out the dialect".
Theatre
In the Screen-to-Stage Adaptation remake of The Producers, three stereotypical Irish cops arrest Max and Leo: O'Rourke, O'Riley and O'Houllihan, the last of these played by a black man. ("I've heard of black Irish, but this is ridiculous!")
One stage production of Animal Crackers also had a black Irish officer.
Arsenic And Old Lace has an Officer O'Hara, a basically competent Officer Brophy and a few other, non-Irish cops.
In West Side Story, the Jets repeatedly mock Officer Krupke with a sarcastic "Top o' the day, Officer Krupke!" even though Krupke and his partner (who are presumably not Irish-American, considering his Mitteleurope surname) display none of the trope characteristics.
Lonigan in Wonderful Town, who with the other cops launches into a song and jig under the impression that Eileen is Irish, too.
The Moon is Blue has Detective-Sergeant Michael O'Neill, Patty's Overprotective Dad. She describes him as being "Irish from way back" and talking in a thick brogue when he gets angry.
Video Games
Psychonauts had a lampshade/parody sequence in the lungfish level, complete with Officer O'Lungfish.
This was subverted in Laura Bow: The Dagger of Amon Ra with police chief Ryan O'Riley. He had the accent, but was rude, confrontational, constantly suspicious of you, and otherwise anything but whimsical. He was also the killer.
Urban Chaos Riot Response had quite a few Irish cops, including an O'Hara, an O'Shaunassy and an O'Riley.
"Bugs and Thugs": First Bugs imitates the voice of an Irish Cop to scare his kidnappers, then a real Irish Cop shows up and repeats Bugs' words exactly.
"Bowery Bugs": Steve Brodie approaches a police officer and says "I'm flippin' me lid! Everybody's turnin' into rabbits!" The officer reveals himself to be Bugs in disguise, who says (in a thick Irish accent) "What's all this about rabbits, Doc?"
In a latter-day Daffy Duck/Porky Pig short, Daffy uses the moniker "Sergeant O'Duck".
There's one that pops up in The Simpsons from time to time. He's usually portrayed as a nice and jolly NYPD cop, but he's seen on Springfield from time to time.
In the "The Simpsons are going to Ireland!" episode, an Irish judge comments that Ireland has gotten nicer since they sent all their incompetent half-wits to America..."Where you, for some reason, made them police officers." Cue Chief Wiggum entering and accidentally macing and tasering himself.
Springfield's St. Patrick's Day parade features a float honoring "2000 Years of Irish Cops."
In the Teenage Mutant Ninja Turtles cartoon from the late 80s and early 90s, there was an episode with an Irish cop who persisted in believing the turtles were leprechauns.
The Justice League episode 'Legends' sends GL, Flash, Hawkgirl and Martian Manhunter to a dimension that's one giant silver age pastiche. Naturally there are exactly two cops in town, both red-haired Irish types with broad accents.
Since the trope is well-represented in the Silver Age comics, it's possible these are shout-outs to specific Silver Age O'Haras rather than O'Haras in the generic sense.
After The Reveal the same cops speak with American accents.
Actually a subversion, since Yates is a relatively realistic, hard-bitten "modern" city cop who just happens to be of Irish descent. His wife, Maggie, however, has the stereotypical immigrant accent.
The New Adventures of Superman episode "The Cage of Glass". When Brainiac shrinks Metropolis, one of the city police officers is this stereotype.
The Color Classics short "The Fresh Vegetable Mystery" milks this trope for all its worth. The short "A Kick In Time" also has a gag with an irish police horse appearing.