Ciel and Sebastian from Black Butler sum just about everything that happened during the murder mystery arc and how it was to the Wordsmith Arther.
At the end of the first arc of Fables, Bigby Wolf, the Fabletown sheriff, gets to do one of these about Rose Red's not-murder, calling it the "parlor room scene" and explaining that it's basically every detective's dream to actually perform it.
Done by Gabe in just about every issue of The Maze Agency. Occasionally lampshaded by having another character think they've solved the mystery and do the summation, only for Gabe to explain why they are wrong and provide the true solution.
The best summation ever was conducted by Tim Curry in full maniac mode at the end of the movie Clue, and included as much reenactment of every single event of the evening as he can very humorously manage.
It's also a bit of a subversion, since his summation is not really helpful in identifying the killer. In fact, in two of the Multiple Endings, his explanation of how the murders of Mr. Boddy and the cook were committed is flat-out wrong.
Sort of subverted twice in Hot Fuzz. Once where Sgt. Angel confronts Skinner, and lays out why he thinks he's committed the murders; subverted in that nothing comes of it, because as it turns out Angel's wrong on a few points, which (for the moment) exonerates Skinner. The second time is a Summation by the Neighborhood Watch Alliance, a subversion because it's the culprits giving it to the hero, who's just shocked and amazed by the meager justification they had for killing people.
Subverted as part of the infamous plot twist at the end of The Usual Suspects. Agent Kujan believes he has figured out that Keaton was Keyser Soze and explains this to Verbal Kint, complete with revelatory montage. The explanation seems to hold water and Verbal is allowed to go. But seconds later, Kujan realizes that Verbal's story, from which Kujan created his explanation, was completely fabricated—Verbal himself is Keyser Soze.
Subverted in Resident Evil Degeneration, where Claire is making one at Senator Davis, explaining his motives for causing the havoc in the film...until Leon shows up and says someone they apprehended earlier has spilled the beans, and Senator Davis is entirely innocent, if still a sleazebag.
A Shot In The Dark. By the end of the movie Inspector Clouseau still hasn't been able to work out who the killer is, so he gathers everyone in the one room and starts giving an overly long summation of how he detected the killer, while ordering his deputy to turn out the lights at a particular time so the guilty culprit will panic and flee. Because their watches haven't been synchronised Clouseau has to ramble on for so long the guilty parties start confessing anyway (it turns out everyone in the room commited one crime or another) so when the lights go out they all flee and get blown up by a car bomb meant for Clouseau.
In Dial M For Murder, one of the characters gives the summation as a purely hypothetical imagining of what could have happened, not realizing that that is exactly what did happen.
Brick has the protagonist, Brendan, giving it to the mastermind behind it all, to prove they're well and truly caught. He only gets one detail wrong: the intended result.
The 2009 film of Sherlock Holmes uses this trope. The Detective does this almost constantly—he doesn't even wait until the end of the film! This is because this is how Holmes' mind works—he is constantly analyzing things to their conclusion.
The first Mission: Impossible film showed Ethan Hunt's internal summations (there are two possible solutions, depending on whether or not there was an accomplice) during a conversation with the Big Bad, while Ethan is verbally agreeing with the Big Bad that someone else did it.
The Harry Potter series: Harry gets one in The Chamber of Secrets, near the end, he explains to Ron what the monster is and how it's been getting around the castle, having figured it out from the torn page they found in Hermione's hand.
Fandorin also has a related one where he sums up the evidence with "(Statement). That is one. (Statement) That is two," and so forth, but this is usually part way through while he is still considering hypotheses.
Isaac Asimov loved this trope, because he loved to write neat little stories with perfect logical solutions. Pick any Asimov short story, there's a 90% chance it'll contain one of these.
If not the Ur example., definitely a codifier for the trope: The Sherlock Holmes books are almost nothing but this trope.
Not exactly a crime, but at the end of Stephen Fry's novel The Hippopotamus, the narrator, Ted, gives a brilliant summation of how all of David's so-called miracles were not his responsibility at all.
Live Action TV
This occurs in nearly every episode of Monk, usually from the title character. Hence we should probably call hi the Trope Codifier. The line "Here's what happened" is normally used for these and is used in almost every episode (or possibly every episode)
This was hilariously subverted on "Mr. Monk and the Garbage Strike": Monk, driven insane by a garbage strike, does the summation line before a telling an insane story about Alice Cooper murdering a man so he could steal his antique wingback chair.
Another good one is in "Mr. Monk Gets Cabin Fever": while pinned down by sniper fire, Monk and Randy each get their Eureka moment at the exact same time, and say in perfect unison, "Oh my God, I've got it! Here's what happened:"... then the camera jumps back and forth between their summations.
Or the one where Monk becomes traumatized because of an earthquake, and does the entire summation in gibberish. You can still kind of tell what he's saying because the show still gives you flashbacks to the crime.
The show tends to make this a gag about once every ten episodes: for instance, Randy explains it in Monk's style, complete with flashbacks, to a rookie officer, who then explains she already heard it from Monk.
"Mr. Monk Visits a Farm" does a similar variant: Randy gives the summation, but Monk had fed it to him by impersonating his self-motivational CD while he was sleeping. Monk has to prompt him to continue when Randy doubts himself partway through.
The Summation is Lampshaded and parodied in the 100th episode special. When James Novak interviews Jimmy Belmont, Joey Krenshaw and Hal Tucker, all of whom were put away by Monk (in "Mr. Monk Visits a Farm," "Mr. Monk and the Daredevil," and "Mr. Monk Makes a Friend"), they complain that they found the Summation tedious, because Monk was basically reciting what they already knew (they were the criminals, after all!).
Lampshaded again with the CSI: Crime Scene Investigation parody episode "Mr. Monk and the TV Star". Captain Stottlemeyer walks into the editing room of a clear CSIExpy while Brad Terry is helping put together the Summation scene of the episode they're working on:
Captain Leland Stottlemeyer: This is my favorite part, where everyone stands around and you sum up the case.
Brad Terry: Thanks.
Captain Leland Stottlemeyer: I wasn't talking to you. I was talking to Mr. Monk.
Subverted in the episode "Mr. Monk Goes to Jail," when Sharona does the Summation instead of Monk.
Parodied in one episode when Monk has to join a therapy group and the members keep getting killed off. When Monk tells the rest of the group about the possibility of the deaths being homicides, Harold mimics Monk's investigation style and then goes into a The Summation-slash-Hannibal Lecture in which he points out that Monk had motive, opportunity, and a advantegeous position complete with fake flashbacks that portray Monk as an Ax Crazy psuedo-Yandere who wants Dr. Bell all to himself (Harold was right about the last part). This is effective enough to make Monk himself seriously consider that he might be unconciously killing people.
Parodied in "Mr. Monk and Sharona" where Monk, being rushed by Sharona, literally gives his summation in fast motion, complete with squeaky fast forward (or as he says, picture-go-fast) voice distortion. Unable to understand a goddamn word, he's asked to repeat it at regular talking speed.
Some fun is had in Mr. Monk and the Birds and the Bees when Natalie says "I've been waiting a long time to say this..."
In "Mr. Monk Gets Drunk", he attempts to deliver The Summation while drunk, having accidentally drank an alcoholic wine (which he believed was non-alcoholic.) It goes about as smoothly as you'd expect.
In "Mr. Monk and the Kid," it's read in the form of a bedtime story. And it really works.
In "Mr. Monk and the Miracle," Monk and Natalie disguise themselves as nuns to sneak into a monastery to rescue a converted Captain Stottlemeyer. It's funny because they actually have to harmonize their voices to blend in the summation. You get your usual flashback shots, but Monk and Natalie are speaking in emotionless bass voices. Natalie sounds like she's trying to speak a tenor.
A subversion occurs in an episode of New Tricks, in which one of the squad explains how a suspected arsonist didn't burn down his factory; the explosion and fire was caused by an accident gasleak and a spark from the ringing of his mobile phone, which he had accidentally left behind.
Columbo is fond of this method, explaining to the perp of the week exactly how they tripped up.
Rarely done on Shark, except for the time that Stark turned a suicide into a murder victim and framed a guy.
Once an Episode on Jonathan Creek, following the obligatory Eureka Moment. In an interesting twist, the very first summation that Jonathan ever gives, in "The Wrestler's Tomb", is promptly shot down by the man himself about ten seconds after he's finished giving it, when he points out that while his solution is possible, it's hardly plausible. His second, at the end of the same episode, is more conventionally handled.
Spoofed in an episode of Angel, where the actual mystery plot takes place entirely offscreen, but the audience is nonetheless shown Wesley giving one of these to the gathered suspects at the end. The story he tells is long and complicated, featuring fraud and lies and betrayal, and when it is all over Gunn actually says that the entire scene was really damn cool. It makes you really wish we got to see the investigation.
Wesley admits afterwards that when he started the summation, he wasn't sure who did it. He just kept talking and going over the evidence until it made sense.
Psych typically has two: first Shawn's BS-laden explanation to the police of what's happened and how to prove it, and then his explanation to Gus and/or Henry of how he figured it out.
Parodied in It's Always Sunny in Philadelphia when the gang is trying to figure out who keeps pooping in Charlie and Frank's bed. At the end of the episode, Artemis gives a long summation showing that each member of the gang is guilty. Frank then denies the story and admits that he did it all, because "poop is funny." He even pooped on the floor while Artemis was making her summation.
Ellery Queen (NBC, 1975) always had oneNo Fourth Wall moment every episode. Immediately following Ellery's mandatory Eureka Moment, he would turn to the audience, briefly review the key evidence for the viewers, and ask them if they'd figured out who the culprit was. This came from the Ellery Queen books, where the authors would stop at some point and tell you that you now had enough clues to prove who the murderer was. After that, Ellery Queen would do the big 'one of you is the murderer' speech and solve the murder.
Generally averted in City Homicide, where the team works it out between themselves. Some exceptions include Sparkes' interview with Frances Deerborne in "Family Planning" and Rhys deducing what happened to Gisela Goldberg in "Gut Instinct."
Dangan Ronpa requires the player to put together the summation themselves in the form of a manga that is missing panels. Evidence is used to fill in the gaps in the story, and once everything is in place the main character will walk the others through the crime. This phase of the game called "Climax Inference".
Due to the story of Persona 4, this happens multiple times over the course of the game, with different twists based on the evidence you get. The second to last one is done by the killer themself, and fantastically tears down the entire structure of the case thus far.
The Ace Attorney games have this. Except for case 1-4, they are set to that games version of "Announce the Truth."
Related to the above, Umineko No Naku Koro Ni has this at the end of the fourth arc. It's subverted, since Battler's explanations for the mysteries are completely wrong, and though he defeats Beatrice he isn't even close to the truth.
Also, the Court of Illusions in the fifth arc, and the Will versus Claire battle in the seventh.
At the end of the murder mysteryvisual novelJisei, you must correctly pick out the correct order that the suspects arrived, the cause of death, and finally, the identity of the murderer.
Subverted in the Whateley Universe Story solving Reach. It was For the sole purpose of getting the bad guy to flee, scared stiff, and reveal where she kept the hostage. The Summation, however, was real. They just needed that last info. (And the bad guy needed to accomplish his/her plan.)
Scooby-Doo. Providing the Summation is part of Fred Jones and Velma Dinkley's job description on the show.
Bart (and sometimes Lisa) from The Simpsons, gets to do this, displaying uncanny reasoning skills you wouldn't associate with him, whenever Sideshow Bob shows up, notably in his first two appearances when he frames Krusty for robbery and tries to kill Selma. Even though his third appearance in the episode Cape Feare isn't so much of a mystery plot, but has more of a straight forward "I'm coming to get my revenge!" premise, Bart still tells a gathering at the end of the episode how he managed to distract Sideshow Bob.
There's also "The Great Money Caper", where it is revealed that Homer and Bart's entire comeuppance was staged by Marge and Lisa. Homer then realises the implication that the police force, the TV news, a courthouse full of people, and a popular entertainer had nothing better to do than to help deliver An Aesop to them. Lisa starts to tell him "a simple and highly satisfying explanation", but everyone goes surfing instead.
Larry on Clue Club does this once he has all the suspects in one room with Sheriff Bagley waiting to hear whodunnit.
In the Futurama episode "Dial L for Leela" (part of "Anthology of Interest I"), Dr. Zoidberg investigates the murders around Planet Express, eventually calling everyone into the accusing parlour to reveal a boot print on Professor Farnsworth's lab coat and Amy Wong's corpse in a clock. Throughout the summation, Leela (who is an impulsive murderer in this story) keeps turning the lights off right as another character (Cubert Farnsworth, then Scruffy the Janitor, then Nibbler) is about to reveal the murderer, with said character revealed to be stabbed upon the lights coming back. Eventually, Zoidberg recieves a letter from Bender (who also had been killed) revealing who done it.
Zoidberg: My God, it can't be! The murderer, it was— Fry:(yawns) I'm bored. You're boring, Zoidberg; I'm gonna go watch TV. Leela: Could you get the lights on your way out? (Fry turns the lights off.)