A Subtrope of The Summation, this commonly occurs at the end of a murder mystery.
All of the suspects gather together in a room, so that the detective can tell them who the murderer is. The detective goes down the list of suspects one by one, explaining why they are innocent - although some of them may be guilty of other, minor, crimes. Eventually he will get to the guilty party, and explain how and why the murder was committed.
Expect at least one embarrassing secret to be unearthed during this scene.
Common stock phrases in these scenes:
"I suppose you're all wondering why I've gathered you here..."
"Someone in this room... is a murderer!" May be followed by a Scare Chord.
The Kindaichi Case Files ends every story arc with one of these, although they rarely happen in a parlor, instead usually occurring in the same place where one of the victims was killed. The summation is usually accompanied by a dramatic explanation of exactly how the killer carried out his crimes. Kindaichi will explain everything — motive, method, all the secrets behind the case — without revealing the killer's identity, leaving that for the very end.
Case Closed. Played with a lot since Conan, as a child, has to use Richard as a sort of mask in order to reveal the truth, by knocking him out, slumping him over something for a generic "deep thought" pose, and using a voice-changer to talk like him. Not always the best idea since sometimes, these suspects aren't very willing to just stand and watch the man reveal everything.
Parodied in Neil Simon's Murder by Death. Lionel Twain calls together the world's five greatest detectives and issues them a challenge: to solve a murder that hasn't yet occurred. At the end of the movie, they go through this trope five separate times, as each detective claims to have solved the murder and tries to prove that they're right.
In The Thin Man and The Thin Man Returns, Nick Charles solves the mystery by this method. In the first movie, by his own admission, he hadn't quite sussed who the murderer was; he'd ruled out most of them, so he laid out the facts until one of the remaining suspects fit, and made an accusation.
Happens in each of the Albert Finney/Peter Ustinov Hercule Poirot movies. This includes Death on the Nile, even though the book just had Poirot explain his conclusion to the killers and a couple of others, not the whole boat.
Agatha Christie novels are known for this: Hercule Poirot almost always does it; so does Miss Marple. However, Tommy and Tuppence Beresford rarely do and Parker Pyne almost never does. Tommy and Tuppence's investigations tend to be usually messier and more convoluted, and Parker Pyne, when his job of "making people happy" involves investigating a crime, prefers to be subtle about it. Christie's Summation Gatherings frequently also mark the beginning of a romance, and sometimes the end of one.
Nero Wolfe virtually always does something like this. It's not in the parlor, though, it's almost always in his office instead. In the few stories where he's had to leave his house, and resolve the case before he can return to it, the Summation Gathering takes place in whatever place is appropriate:
In Too Many Cooks, it is held at the banquet table at the Kanewha Spa, following the final feast of Les Quinze Maîtres.
In Some Buried Caesar, it takes place at Thomas Pratt's home in upstate New York.
In Immune To Murder, it takes place at O. V. Bragan's fishing lodge in the Adirondacks, where he has gone to make trout Montbarry for a foreign ambassador at the special request of the US Secretary of State.
In Too Many Detectives, it takes place in a hotel room in Albany, where he has been summoned to submit to questioning in a state investigation of illegal wiretapping.
In The Impolite Corpse (from the third radio series), it takes place at the murder scene because his client told him over the phone that Archie was in danger. Wolfe suspects (correctly) that this was a lie intended to get him over there, but had found the case so annoying that he was willing to just solve it right there and be done with it. Incidentally, the fact that his client went to such lengths to make him leave his office is the pivotal clue that breaks the case.
In Randall Garrett's Lord Darcy homage to "Too Many Cooks", Too Many Magicians, the Summation Gathering takes place in the Nero Wolfe-analogue's office, but it's conducted by Lord Darcy. However, the Summation Gathering is actually an elaborate misdirection to get the real murderer to give them his sword to reenact of the murder, so he'll be unarmed when they arrest him.
In Glen Cook's Nero Wolfe-inspired Garrett, P.I. series, this happens at Garrett's house in Cold Copper Tears, and at the brewery in Faded Steel Heat. In a variant, the gatherings aren't just an opportunity for the sleuth to explain his deductions, but also for the Dead Man to use his mind-reading powers on the culprits and any accomplices.
In Vernor Vinge's Marooned In Realtime, the detective Wil Brierson calls most of the (decimated) world's population into a meeting hall to accuse the suspect of murder. The character is not only aware of the trope whilst doing it but is worried about a horrible variant he read about: detective gathers the suspects into a room then applies a definitive test to all the suspects: all suspects are guilty. Unmarked grave for detective, happy end for the suspects.
Used in the Forgotten Realms novel Murder in Cormyr, when retired wizard Benelaius uses this setup, which his servant Jasper notes as coming from a series of detective novels Benelaius claims to despise, to expose a man guilty of espionage, attempted mass murder, and (of course) murder. Subverted in that Benelaius arranged for the murderer to sit somewhere where he could make an easy escape and flee into exile rather than face death as Benelaius was a pacifist. Also subverted in that while the first two accusations were true Benelaius knowingly framed the accused for the actual murders so as to cover up the real murderer's guilt.
Peter Tremayne's Sister Fidelma does this in every single novel, often drawing together bitter enemies who otherwise wouldn't be caught dead in the same room. She seems to be constitutionally unable to explain herself without every single character present, even if she has to browbeat a king into gathering these characters for her.
In the Angel episode "Happy Anniversary" Wesley does this to determine which of the family members summoned a demon. Notable because the entire rest of this B plot happens off-screen, although it sounds absolutely fascinating.
The Doctor Who episode "The Unicorn and the Wasp" has Agatha Christie herself solving the mystery, but it's Played for Laughs thanks to Donna, who hasn't quite caught on and keeps accusing the wrong person.
A variant in the Veronica Mars episode "An Echolls Family Christmas": She figured out who stole the game pot from the poker game, and suggests that they all show up for another game, and whoever is revealed to have stolen it will be kicked out and will have effectively bought her into the game.
A subversion appears in NCIS, during the sting operation that identified Agent Lee as The Mole. Having summoned every potential culprit together, the Director has their hands tested for evidence, and identifies the innocent Abby as the guilty party, allowing the team to follow the actual suspect once the fake one is in custody and the Mole thinks the internal investigation is over.
Lampshaded in Tropical Heat, when the detective, Nick asks that the suspects be gathered in one room, and his friend Spider asks derisively if he's going to do "that whole Agatha Christie summation thing".
In an episode of Seinfeld, George plots an elaborate setup to prove a mechanic stole his Twix bar. It's ruined when he leaves the room...
Saleswoman: Hey Willy, check it out! Free candy!
George: That's my candy lineup! Where are all my cards? They're all on the floor! And you! How many Twix does that make for you today? Like eight Twix?
Man: Hey, this Clark bar is good!
George: It's a Twix! They're all Twix! It was a setup! A setup, I tell ya! And you’ve robbed it! You’ve all screwed me again! Now, gimme one! Gimme a Twix!
Standard way Shawn and Gus close a Psych investigation.
Parodied in The Conditions of Great Detectives as Tenkaichi demands a dramatic enough summation at the end of each episode to keep the audience happy. Fujii felt that calling people who were clearly not the murderer and not involved to the summation, so there's only two people at the end of the first episode. Tenkaichi refuses to explain who did it until enough people are gathered (including a girl walking her puppy) and even then he didn't get a chance to reveal who was the murderer. Afterwards everybody leaves before he can explain how the Locked Room Mystery occurred except an old woman who didn't understand why anybody should care.
Parodied on an episode of Frasier when Frasier Crane calls together Niles, Daphne and Martin to reveal who is guilty of replacing a tape cassette of one of his radio shows. He exonerates Daphne and Martin and is about to accuse Niles when Daphne suddenly confesses. When Frasier shouts out, "A-ha!" Niles snarks back, "You don't get to say 'a-ha,' you thought it was me."
The early Mash episode "I Hate a Mystery" combines this with Bluffing the Murderer, although the crime in question is theft rather than murder.
In another episode Hawkeye jokingly invokes this while watching a home movie of Frank Burns' wedding, as several of Burns' relatives are shown standing together onscreen.
Los misterios de Laura. Since Laura is a 20 years younger Miss Marple working at the police, she does that every time. Even in the couple of episodes when he quits the force.
Suspect: Why do we have to listen to a random person telling us we are all a bunch of murderers?
Chief Detective: Because I allow her to say whatever she wants.
Likely Suspects and the remake of Burkes Law had this regularly, of the type where the detective deals with the innocent people by accusing them, and then revealing the "accusation" to be a Bait-and-Switch Comment.
In an early quest of Baten Kaitos Origins, the characters are investigating a series of terrorist attacks from a neighboring town, and hold several of these as new information comes to light.
Professor Layton (chiefly the games, though there's a spectacular one in the movie) have these, though they never really bring closure to the mystery, since the Big Bad always runs off before they can be apprehended.
Subverted in Episode 5 or Umineko no Naku Koro ni. All the elements of the trope are in action, including the revealing of the culprit's shameful secrets. Except a tiny, insignificant detail… the "obvious culprit" is actually innocent. Not that the Episode's detective has the slightest concern for such trivialities.
In a parody in the Futurama episode "Anthology of Interest I", this was referred to as "the accusing parlor". It appears again in "The 30% Iron Chef".
Farnsworth: TO THE ACCUSATORIUM!
A teaser to Batman: The Brave and the Bold was in set in one of these to discover who stole a gold skull. Turns out almost everyone was lying about something anyway. It was False Face who took the skull.
Daffy tries this on his neighbors in The Looney Tunes Show episode "Newsapaper Thief." His failure to plan ahead means that he has to constantly intervene to correct errors in his planning.
Near the end of the My Little Pony: Friendship Is Magic episode "MMMystery on the Friendship Express", Twilight Sparkle calls for one of these after finding clues to who sabotaged the cake Pinkie Pie was guarding.
Mulia: Erm, why are we all here again? Twilight: (entering the room) I bet you're wondering why you're all here again. Joe: She's good.
Done again in "Too Many Pinkie Pies" after the Pinkie clones have been rounded up in the town hall.
Animaniacs's Hercule Yakko has fun with this: Yakko dramatically whispers he knows the location of Marita's missing diamond and orders the ship's passengers to be assembled in the State Room: but not to reveal the thief, but because he didn't have enough people to play charades, and also to say none of them took the diamond, but he will turn the room upside down to prove the diamond is there; once everyone has fallen to the ceiling the diamond appears; Marita was sitting on it the whole time