Someone has been captured by their enemies, usually a group with distinct personalities and backstories, like a Quirky Miniboss Squad, who operate on more or less equal terms with each other (as opposed to a singular Big Bad and a collection of Mooks).
This character is well known to his captors. They are careful not to give him any obvious openings — they disarm him, disable his powers, lock him up, and keep guards on him at all time. Escape by brute force isn't going to work, as he's seriously outnumbered and lacks access to his weapons and abilities. Without resources, MacGyvering up a solution isn't going to work, either.
How will he escape?
He sits back, pretends to accept his fate and engages in surreptitious psychological warfare against most or all of the members of the enemy group. Engaging them in idle conversation, he plants the seeds of discord, playing on the ...
... egos - "How can you take orders from that buffoon? You should really be the one in charge."
Gundam Wing: One of Relena Darlian's specialities. Early in the story she convinced a certain Hitman with a Heart with a gun not to shoot her to death... and then she roped him into dancing with her at a high-class party!
Attempted by Kagome Higurashi from InuYasha, when she was kidnapped by Manten and Hiten. While she didn't secure her release, she did manage to keep herself alive until Inuyasha came to fight them.
When Quinton Zempfester is imprisoned by trolls in Thieves & Kings, he talks his way out by excitedly greeting one of the trolls as the spy sent to free him, thus creating suspicion among the other trolls that he is a spy, and setting in motion a self-fulfilling prophecy, as the hapless troll finds that he is doomed to torture for his imaginary spy secrets if he does not go rogue and flee immediately. Rather than face this fugitive fate alone, Quinton offers the troll his assistance, if released, and the two make a break for it together.
In X-Men Unlimited # 47, Cyclops wakes up after a fight with an army of generic Black Ops Ninjas to find himself strapped down and about to have his eyes cut out by a low-on-ethics surgeon. He calmly explains to the surgeon that he'd better remember to kill him when he's done, because he's memorised the brand of the surgical equipment in the room and will be able to track him down by it. Oh, and even if he is dead, there's a telepathic redhead who will be looking for his killers. Either way, the end result will be a conversation with Wolverine. The surgeon lets him go, requesting a light beating to justify the escape. Cyclops is happy to oblige.
Lucifer: In "The House of Windowless Rooms", a demonic assassin is sent against Lucifer while he's powerless and mortal. The gods who sent the assassin remark that she's obviously failed, as Lucifer has had enough time to start talking to her, which is all he needs.
The Authority were engaged in a battle with psychotic super-soldiers engineered by the government at one point, and their resident Badass, the Midnighter, was trapped under some rubble and about to be obliterated by one of them. In a few sentences, he essentially deconstructed the soldier's life and forced him to realize what a failure he was. The soldier paused, removed the rubble, handed the Midnighter his helmet, and walked away from the fight. At the end of the story arc, the Midnighter even gets a letter from the guy, thanking him for helping him out of his self-destructive situation and telling him about his new wife and kids.
Subverted by Empowered, who spots a life-threatening aneurysm in the head of the mook who's guarding her, using her suit's X-Ray Vision. The mook doesn't believe her at first and thinks she's trying to pull this, but she is dead serious and convinces him to go to the hospital; she just didn't want anyone to suffer the same fate as her father.
John Constantine has been known to escape from really dire dangers using this tactic. A full and almost flawless con man, he's always tricking demons, angels and monsters, and even criminals and ruffians, into distrusting each other until they kill themselves.
Shadowfax tries this in You Obey. It backfires spectacularly, and also marks the moment when the story gets serious.
At one point in the Twilight AU fic Luminosity, sensible!Bella, still human, has been kidnapped by the evil vampire James, who's probably going to kill her because he wants to make Edward suffer. Bella's only chance to survive is to talk James into doing something stupid, and it works: she lies to him, saying that no, Edward doesn't care about her and was going to give her over to The Volturi because they give out rewards in exchange for humans with special powers. James believes her, and takes her to the Volturi. They're not too happy with James...
Pistols, cannons and swords pale in comparison to this trope's power in Pirates of the Caribbean. Jack Sparrow can talk himself out of any situation, and he seemed to have fun teaching the fine art to Will and Elizabeth. Best examples are Jack talking Norrington's sword from his throat to Will's, Jack talking himself out of a Deal with the Devil, bribing help from his enemies several times, and convincing Will that he should help Jack find the key to the Dead's Man's Chest "Because the finding of this finds you incapacitorially finding and/or locating in you discovering, detecting of a way to save your dolly-bell, oh.. whats-her-face?"
Interesting side note: Jack doesn't just use this tactic, he relies on it, and in the course of three movies, with all the great escapes he pulls off, he only escapes once all by himself, and only by forcing himself to think like Will.
In Moonraker, Bond uses Hugo Drax's speech to inspire a Heel-Face Turn in Jaws, who takes notice of how much he and his short, bespectacled, braces-wearing girlfriend stick out amongst Drax's future "Master Race".
In Goldfinger, Bond uses this to get out of Goldfinger's Death Trap. He reminds Goldfinger that there are other agents out there who will replace him if he dies, implying that his death would give the rest of MI6 an excuse to move against him immediately.
Done by The Joker in The Dark Knight. After Batman and Commissioner Gordon leave, he is left alone in the interrogation room with one of Gordon's detectives ... at which point The Joker goads the policeman into attacking him by explaining his motivations for killing six of that detective's friends. At which point, he makes his escape. What makes this a truly interesting case is that the detective was warned beforehand that the Joker would use this tactic on him, and not to fall for it. The problem is that the Joker is just that good at manipulating people.
At the beginning of the film, one of the bank robbers realises that their boss has given each of them orders to kill one of the others once their part of the plan is complete, and tries to talk the last of his fellows around by pointing out that their boss will do the same to him. Unfortunately, the last robber isthat boss.
In Cars 2, when Mater is surrounded by a pack of Mooks, he tries to invoke this by sympathizing with them as outcasts and laughing stocks. It doesn't work.
The President's Analyst, a fugitive from his job, ends up captured by a Soviet agent, who is a pretty decent guy (he'd just rescued the doctor from being assassinated) but is determined to bring him back to Russia. The doctor engages the Russian in casual conversation, and soon gets him to realize he'd only become a spy out of fear of his Stalinist father. He abandons the idea of taking the doctor to Russia, figuring he needs a few years of analysis.
Done in Idiocracy by the protagonist, who's a completely average guy by modern-day standards but a genius 500 years from now. When arrested and taken to jail, he manages to convince a cop to let him go by telling him... that he should be in the "released" line. Given how degraded humanity is, it works.
In The Three Musketeers, Milady De Winter is imprisoned by the Duke of Buckingham under the care of John Felton, and not only convinces Felton to free her, but also to assassinate the Duke. As a real John Felton really did assassinate George Villiers, the first Duke of Buckingham, this is also a Historical In-Joke.
Not long before the execution she talks to her guards. The guards seem unimpressed, but musketeers take no chances and replace them.
Later she talks to d'Artagnan and almost convinces him to free her. He has to be restrained.
In Dune, Thufir Hawat, captured by Baron Vladimir Harkonnen's forces and forced to work for him, plays him off of his nephew, Feyd Rautha. Feyd makes a rash attempt (suggested by Thufir) to assassinate his uncle, and the Baron is forced to consider executing his only legitimate heir. Thufir does this more for vengeance and loyalty to his prior liege than for escape, which the Baron ensured would be a fatal endeavor; the Baron works his way out of the dilemma by denying Feyd the governorship of the planet the Harkonnens took from Thufir's old master. Earlier in the book, Paul and Jessica use the Voice to get their Harkonnen guards to kill each other.
In Poul Anderson's Dominic Flandry series, Flandry is an Agent for the Terran Empire. Kidnapped by an alien race, who just assumes he is a decadent worthless low level agent, he soon has the entire leadership of the planet backstabbing each other.
Roger Zelazny's Creatures of Light and Darkness: Set the Destroyer has been taken captive, immobilized, and disarmed by his enemies. Set's gift is the ability to find the weaknesses in his opponents. One of his captors — a priest who is low on faith — is persuaded by Set that by taking Set captive, the priest is an accessory to the murder of God. The priest promptly kills his co-conspirators.
Next of Kin by Eric Frank Russell is the very pinnacle of this trope. John Leeming is the only human being on alien planet inhabited by stocky reptiles. It is a part of union, which is at war with Earth and its allies. He is imprisoned, stripped of all weapons and gadgets, does not know their language (initially)... and he talks his way out. Moreover — he makes all the government of this planet believe that humans have distinct spiritual companions (they do believe in poltergeist, simplifying his work), he is given a spaceship, he is given the means to change it for a more advanced one and reach Earth... and the planet persuades the majority of members of the anti-Earth union to stop the war. Such is the power of diplomacy.
In Diabologic by the same author an Earth scout finds fairly advanced spacefaring aliens. He lets them capture and interrogate him, then persuades them to refuel his ship and let him go (he doesn't want to go home for refueling, he wants to continue exploring). His secret weapon: the titular diabologic, the science of fooling sentient creatures.
Eli Monpress of The Spirit Thief basically has this as his power—rather than needing to form a specific bond with a spirit to gain its obedience, he can just talk to them, and more often than not they'll obey him. His first scene has him talking his way out of a dungeon by convincing the door to fall over.
Miles Vorkosigan of the Vorkosigan Saga runs on this. Unfortunately, some of his adversaries have grown somewhat Miles savvy. From The Vor Game:
Admiral Oser: Space them. ... Use the portside access lock, it's closest. If he, [pointing to Miles] starts to talk, stop his tongue. It's his most dangerous organ.
Miles: Aren't you even going to have me chemically interrogated?
Oser: And contaminate my interrogators? The last thing I want is to give you rein to talk, to anyone. ... Whatever your planned speech, removing your air will neutralize it. You nearly convinced me.
While most of the Aes Sedai are not her enemies, Egwene's capture and imprisonment in the White Tower in The Wheel of Time is otherwise this trope. By the time she is made true Amyrlin of the re-unified Tower, she has not only subverted and won over all the novices and most of the Accepted, she has earned the admiration of her disciplinarian, the Mistress of Novices Silviana (who then becomes willing to stand up to Elaida and the Hall on her behalf, facing birching, death, or stilling); proven to the Aes Sedai she truly is the leader, thinker, and rallying point she claims to be until each Ajah Head wistfully wishes (or outright offers) that she had joined or would join their Ajah; gotten them to admit they had unlawfully raised Elaida (since some of their number had been Black); and out-debated and completely underminedElaida herself. And while she doesn't turn the Ajahs against each other (in fact her main thrust is trying to undo such division as Elaida and the Black had done, bringing the Ajahs together again), she does turn a large number of them against Elaida. If she hadn't been taken by the Seanchan, she would very likely have been pulled down, tried, perhaps even executed.
Tyrion Lannister of A Song of Ice and Fire runs entirely off this trope. As a dwarf in a medieval society, the best he could hope for was to be made a jester or be part of a freak show, or just as likely have been left to die as a child. However, he has the good fortune of being born to the richest house in the kingdom and being one of the smartest characters in the series. The times he has talked, bribed, or conned his way out of death or worse number in the dozens.
Live Action TV
LOST When Ben (or "Henry Gale," as he was identifying himself at the time) was "captured" by the main characters, he spent much of his time turning Locke and Jack against each other. This aided his eventual escape but it alos aided a much longer term and confusing plan.
Firefly: We learn in a flashback that the greed approach not only allowed Mal and Zoe to get out of a violent situation, but resulted in Jayne joining their crew.
One episode involved him breaking up Hal's folk(?) band, The Gentleman Comers, only saying one sentence to each member. Note that he wasn't really trying to get out of anything, he was just manipulating them because he was bored.
The Doctor is a dab hand at doing this. The Seventh Doctor in particular has a knack for it; in "Paradise Towers", he escapes an execution by convincing his over-bureaucratic captors to let him escape.
Then there's this scene from "The Happiness Patrol", where he talks a sniper out of shooting him at point blank range.
He tries it again on the Master in The End of Time Part 2 by giving him a speech on how "stone-cold brilliant" he is. His description soon switches to "bone-dead stupid" because the Master doesn't realise his right hand man is really a Vinvocchi.
Scorpius talking down Captain Crais' bodyguards in Farscape:
I commend your loyalty. It must be difficult to maintain for an officer like Crais... an officer on the edge and out of control. I have unconditional authority on a Gammak Base. Captain Crais will go to the Chair: to stop that, you'll have to kill me... and all my men. Are you prepared to do that? Do what you know in your hearts is the right thing: put Crais in the Chair.
Daniel Jackson on Stargate SG-1. He managed to talk himself out of being dead a few times, but hey, that's Daniel for you. In later seasons, he comes to rely on this much less, although still proves capable of giving a great Rousing Speech every now and then.
Reid on Criminal Minds tries for one of these at least three or four times a season. They don't always work out, but when they do, the results can be quite spectacular. Perhaps the best example (and a Crowning Moment of Awesome to boot) comes in Season Three, when a serial killer on death row invites Reid and Hotch to interview him just before he's executed. He plans to lull them into a false sense of security and then kill them both in order to derail his trial and buy himself some more time alive. Through careful manipulation of the agents, the timing and the situation, he very nearly succeeds. Somehow, Hotch and Reid wind up alone in a locked room, unarmed, with a serial killer whose bare hands were his preferred weapon, who wants them dead, and who isn't wearing handcuffs. It never becomes important. Reid keeps the serial killer talking until the guards return from shift change. Fifteen minutes later. Not that Hotch's plan to kick the guy's ass manually wouldn't have been fun to watch, but...
It's awesome when it works, but the times when it fails are more interesting, and also generally awful and depressing, because you often really think he's going to pull it off this time...right before someone dies.
Burn Notice This is Standard Operating Procedure whenever a member of Team Westen finds him/herself captured.
Star Trek: Deep Space Nine episode "The Search, Part II" when a group of Jem'Hadar attempts to arrest Sisko and co, Garak talks their way out by pretending to be The Mole and then shooting the Jem'Hadar once they let their guard down. And this was before the Jem'Hadar were allied with the Cardassians.
Artemus Gordon of The Wild Wild West does this with a group of thugs holding him hostage aboard a moving train in "The Night of the Iron Fist." Their leader eventually catches on, but by that point the damage has been done and said thugs begin attacking each other, giving Artie ample opportunity to casually steer them out an open door onto the tracks flying by below.
Deus Ex: Human Revolution: "Social" boss fights are all about this. You can talk NPCs into giving you codes, standing down from a hostage situation, or letting you into restricted areas.
2027: If you are stopped by the Human Horizon agent in Paris, you can lie to him about your identity, saving your life. Meeting him however, causes an ambush to be set up for you later after the Paris Lab mission.
Fallout 2 also lets you foil the Enclave through the gift of gab, though The Dragon will try to block your hasty retreat from the base no matter how slick you are, forcing a confrontation. You can convince the Enclave Mooks to fight him for you, though; after all, he's not letting them leave either.
In Fallout 3 you can convince both the Big Bad and The Dragon into giving up. The former by using self-destruct code or by proving that he is not doing the right thing, and the latter after a heated debate where you convince him that his government has no authority to do what it is doing.
In Fallout: New Vegas both Legate Lanius and General Oliver can be talked into issuing a retreat, the former by convincing him of the unlikelihood of the Legion's long-term survivability/bluffing him into thinking that he'll be walking into a trap and the latter by convincing him that he's lost at this point or, in the Mr. House and Wild Card path, threatening him with your army of Mecha-Mooks and other allies you've made.
Geneforge lets you be a real Manipulative Bastard about this. Join the Big Bad's faction, stroll into his base, convince him that you have repaired the damaged safety equipment that will let him use the Geneforge, bluff him into thinking that he needs to send his bodyguards away, laugh as he fries himself. Bonus bastard points if you then use the real safety equipment to successfully use the Geneforge yourself, and even more if you find the item that lets you break the Geneforge so that nobody else can use it.
Variations on what's described (breaking it after using it, or breaking it without using it) are the only two very good endings in the entire series.
Jade Empire: The Final Boss tries to use this on YOU. If it works, you let yourself be killed, AND doom the world to a horrible, blighted excistance under a heartlessly brutal, immortal dictator who view people as mere things to use at whim. So DO NOT FALL FOR IT!!!
Mass Effect allows you to put points into Charm and Intimidate skills which allow you to talk (or threaten) your way out of some situations that would otherwise end in bloodshed. Towards the end of the first game, sufficient points in these skills will even allow you to talk down the villain, Saren, on two separate occasions, the second resulting in Saren killing himself. It doesn't get you out of a final boss fight, though.
Planescape: Torment does this one almost all the time. Every plot-significant fight bar one can be bypassed, usually through talking; every other fight can be avoided through stealth or running away. This includes the Big Bad, who you can literally talk out of existence.
Darklands allows to win many Random Encounters without a fight, if one of the characters has appropriately high stats. Mind you, scaring off street thugs, refusing to pay tax to a greedy bishop or calming a bear each require a different set of skills. Prayers can boost skills, if a character knows the right saint. Some fights are unavoidable, though.
In Worm, Skitter manages this when captured by the superhero Flechette and her friend Parian, convincing Flechette that her superiors aren't as morally pure as they make themselves out to be and convincing Parian to leave with the simple expedient of a Briefcase Full of Money.
Batman uses this method to escape the Injustice Gang in the Justice League episode "Injustice For All". Features a very rare instance of the Joker being the voice of reason, as he anticipates Bats's strategy but is unable to convince Luthor to let him kill Batman. Even more interesting: Batman plays several cards at the same time, playing on Solomon Grundy's insecurities, playing the sympathy and sex appeal cards with Cheetah, and eventually delivering a bribe to the Ultra-Humanite (which Humanite donates to PBS). Then, because he's Batman, he reveals at the end that he could have escaped any time he wanted to.
When caught and held defenseless by Scarface's gang, Batman convinces Scarface that the one who sold them out was Arnold Wesker, aka The Ventriloquist. Scarface angrily orders his men to kill Wesker, Scarface is Arnold Wesker - he is just a ventriloquist's doll that Wesker uses to manifest his psychotic Split Personality, so the men hesitate and Scarface thinks they are traitors as well. Batman escapes in the chaos and bring the gangsters down.
Teen Titans: Batman passed this skill onto his protegé, as Robin spends an entire second-season episode convincing Atlas' sidekick, Spike, to turn on his master, who treats him like dirt. He succeeds, helping Cyborg save the day when Spike refuses to give Atlas an unfair advantage in their final battle.
Avatar: The Last Airbender: The Genre Savvy Sokka does this when the gaang is captured by pirates and Zuko, convincing the pirates that they'd get a better deal personally handing the Avatar over to the Fire Lord instead of trading him to Zuko for their valuable scroll. Zuko sees right through it, but the pirates take the bait, a fight breaks out, and the gaang escapes during the chaos.
Perhaps this inspired Aang to try this on Zhao four episodes later...It didn't work.
ReBoot. This is Bob's only option to deal with Hexadecimal in the early episodes, since Hex is far more powerful than Bob. When she succeeds in turning the entire city to stone Bob has to convince her that petrifying the city goes against her nature as a chaos virus. To be precise, a petrified city is the opposite of chaotic- it's quiet, predictable, and the same forever. This works and she reverses the effect and lets Bob go.
In "A Dog and Pony Show", Rarity is captured by the gem-obsessed Diamond Dogs. She puts up absolute minimal (physical) resistance but she coerces/complains/whines the whole time. By the end of the episode, just as The Cavalry arrives, the Dogs are begging to be rid of Rarity.
When large groups of citizens were protesting the electoral fraud in the 2000 elections in Serbia, clever protesters who were jailed used this to spread their message on a personal level to the security forces. As a result, they were more lenient in future incidents than Milosevic wanted them to be, and this eventually led to his overthrow.
A brief summary: Yudkowsky is a member of an organization aiming to make any future AI we may build less of a Crapshoot, and when he told people this, one common reaction was, "Why not just lock the AI away where it couldn't do anything and only let it answer questions?" When he replied that the AI would convince its captors to remove the locks, they replied, "They couldn't convince me!" Sick of this exchange, he decided that he had better prove them wrong ... which he did by making them stake cash on them not letting Yudkowsky (who played the AI) out during a two-hour RP session in a private chatroom, and winning three times in a row.