The "captive" was actually a willing guest in the first place, and the apparent need for rescue was a silly misunderstanding.
The intervention caused more damage than the lack of it, as the heroes have destroyed something that will now cause the base to blow up — Nice Job Breaking It, Hero.
Or, worse, the captive had nearly had an agreement for a peaceful resolution with the apparent villain (perhaps the Monster Is a Mommy or otherwise not really evil), and the heroes' attack restarts the conflict and convinces the foe that peace is impossible.
In Bleach, Rukia doesn't want to be rescued from her impending execution; see the above quote. She thinks she deserves to die for killing her mentor, Kaien Shiba, decades earlier (even though he was possessed by a Hollow and effectively already dead). Ichigo doesn't care. Nor do numerous other characters who aid (or in some cases, attempt to aid) in Rukia's rescue.
She also fears for the safety of those attempting to save her, not being genre savvy enough to know that a small band of reckless youth starting out at the bottom of the totem pole of power levels would be able to defeat a large established organization of fighters, many of which have been training for centuries.
Ichigo seems to have really bad luck with this trope. Pretty much every person he's 'saved' hasn't wanted it. In the movies, Hitsugaya says something along the lines of "I didn't ask for your help and I didn't want it," and while Senna does want to be saved, she doesn't seem to want Ichigo to do it. (Until she realizes her death would be The End of the World as We Know It. Also, in the most recent arc, Orihime thanks Ichigo for saving her, but then goes on to say she'll stay kidnapped so she has the chance the erase the Hougyoku.
A minor (and humorous) version of this can be found in Full Metal Panic! with Sousuke and Mao. When Mao was describing how she first met Sousuke and Kurz, she mentions that her first meeting with Sousuke went rather poorly, with Sousuke being ridiculously unfriendly and stand off-ish. And when Kurz starts sexually harassing her (which was mainly just to ensure that she wouldn't choose him for part of her SRT team), Sousuke stealthily goes up to them and stops Kurz by putting his rifle between them. However, this "rescue" doesn't exactly go appreciated, considering the way he phrased it and the condescending way he acted. "That's enough. Your name is Kurz Weber, right? Stop teasing the petty officer. You'll cause trouble for the rest of us."
An interesting case in Naruto. Naruto and Sakura are continually attempting to rescue Sasuke. Not only does he not want in the slightest to be rescued and dragged back to Konoha, he usually attempts to kill his friends for their troubles. Not that they give up. When Sasuke rescues himself from the imminent danger (by killing the then-Big Bad), Naruto and Sakura go on trying to rescue him from himself. The current method seems to be by either killing him or by fighting him and having both sides simultaneously destroy each other.
Early in the movie Vampire Hunter D Bloodlust, the titular character is tasked with rescuing a woman from the vampire Count Meier Link. However, in the midst of his first fight with Meier, he suddenly hears her call out his name. The revelation is enough of a shock to make D break off the fight, since this is when he realizes he never got the whole story: that she was a willing participant in the whole affair, and that the two are actually trying to elope.
A Certain Magical Index: Mikoto met Touma when he "saved" her from a bunch of delinquents who were hitting on her, not knowing that she is more than capable of defending herself. She doesn't appreciate it. He later pulls the same stunt (in the first novel/episode), this time trying to save the delinquents from inevitably getting zapped. Mikoto is even more angry this time because, as revealed in A Certain Scientific Railgun, she was actually playing along with them in order to get information about the Level Upper out of them.
Subverted in an arc in Fantastic Four, in which Reed, Sue and Johnny travel to the afterlife to rescue the recently deceased Ben, only to learn that Ben doesn't want to be rescued, and in fact their attempts to rescue him are seemingly preventing him from entering Paradise. However, it soon transpires that Ben is actually preventing himself from entering Paradise; he's not ready to die, but his subconscious can't admit this to himself.
In an issue of Dv8, Copycat, who suffers from multiple personality disorder, is furious at her teammates for rescuing her from a virtual solitary confinement cell, because her imprisonment allowed her five personalities to integrate, allowing her a brief period of contentment.
In one issue of Doom Patrol, Robotman saves a woman he found in the trunk of a man's car at a gas station. As soon as the coast was clear, he set her down and she started running from him, throwing rocks to impede his movement... turns out she was the guy's girlfriend, and they were trying to spice things up, and it was her idea in the first place.
In The Beginning, a Sonic the Hedgehog comic series, Sally Acorn attempts to uncover the secret to undoing Roboticizer technology using boots specially designed by Rotor. She set up a 'negotiation' with Robotnik, fully expecting him to betray her and roboticize her. Naturally (or rather unnaturally) he delivers, saying that 'machines can't make or break promises' after Sally accuses him of doing the latter, keeping up the act. Sonic, Tails and Antoine arrive on the scene before she is put through the machine however and 'rescue' her. Back at Knothole, Rotor asks her how it went. She promptly explains what happened to him, with Sonic and his compatriots very confused at her displeasure. She storms off after Rotor tells them what the boots were for.
In the Carl BarksDonald Duck story "Race to the South Seas", news that Scrooge McDuck was lost at sea drives him and his lazy jerkass cousin Gladstone Gander to race each other to the rescue. Natrually, Gladstone reaches Scrooge first, but Scrooge explains he got himself lost at sea to get away from relatives, and cuts him out of his will. Donald, who was nearby, wisely kept himself out of Scrooge's sight.
In the City of Heroes tie-in comics, Statesman went missing at a time the world needed him most (Everyone's super-powers and technology had gone kaput). So the remaining Freedom Phalanx members disobeyed his direct orders (given via a recorded message) and set out to find him. They discovered him being tortured by several former super-villains, and rescue him. His thanks? Calling them all idiots and informing them that he had HIRED those villains and WANTED to get tortured so that he'd have the means to reactivate his powers (somehow). Oops.
In the "Flight of the Firebird" arc in Suicide Squad, the Squad is sent into Russia to free a dissident writer from The Gulag. After breaking her out, they discover that she did not want to be rescued. So long as she was in prison, she was a symbol to other dissidents. If she escaped, she became just another defector. Ultimately she was killed during the escape attempt, thus becoming a martyr.
The furry comic, Xanadu has Tabbe Le Fauve captured, stripped and thrown into the Unicorn Pool. Considering that the beautiful and randy unicorn Empress Alicia then joins him for some sex, Tabbe obviously is in no hurry to be rescued for a while. Unfortunately, that is exactly when his partner, Johathon the mule, gets him out of the pool and the arms of Alicia with Tabbe howling, "But I don't want to be rescued!"
In With Strings Attached, the four rescue about 40 people from being shrunken pets in a basement terrarium, and take them back to C'hou... but they forget to mention that C'hou is in a completely different universe, and it's a one-way trip, so now the refugees are permanently separated from their homes. For the rest of the book, they refer to the four as kidnappers.
In Faith And Doubt, everybody tries "rescuing" Twilight from the phantom giving her dark powers. Twilight is horrified by the thought, because she is Not Brainwashed and is happier with her new abilities.
Film - Animated
In Shrek, Fiona, though at first pleased to be saved, no longer wants to be after it is revealed that her rescuer is an ogre, and will not leave until Shrek forces her to.
The Incredibles has Oliver Sansweet, who sues Mr. Incredible for foiling his suicide attempt.
Oliver Sansweet's Lawyer: Mr. Sansweet didn't asked to be saved. Mr. Sansweet didn't want to be saved. And the injuries received from Mr. Incredible's "actions", so-called, causes him daily pain.
In the final scenes of Ice Age 2: The Meltdown, Sid the sloth resurrects Scrat the squirrel from a Near Death Experience, in which Scrat had experienced the squirrel version of heaven: thus, Scrat proceeds to attack Sid for "saving" him.
In Toy Story 2, Woody at first wants to escape Al's penthouse and return to Andy's home, but after learning about Jessie's abandonment story, and with encouraging words from Stinky Pete, he couldn't bring himself to make an Air-Vent Passageway escape and abandon his Roundup Gang. When Buzz and his rescue team arrive, Woody tells him that he's accepting his fate as a display in a Japanese toy museum, but has second thoughts after Buzz leaves.
Sir Galahad was clearly reluctant to leave the nymphomaniac-populated Castle Anthrax in Monty Python and the Holy Grail. It was apparent the rescuers were protecting his chastity (his title is Galahad the Chaste).
Also, sir Lancelot goes and slaughters a wedding party to rescue a damsel lad in distress, to the horror of the king. Lancelot is then married off to the bride-to-be as compensation for the damage.
In Quantum of Solace, James Bond rescues Camille from the boat of the evil General Medrano, knocking her unconscious in the process. Later he finds out that her being on the General's boat was the culmination of her lifelong plan of revenge on the General for raping and killing her family. Needless to say, she wasn't happy.
Harvey Dent isn't at all happy in The Dark Knight when Batman saves him instead of his would-be fiancee, Rachel Dawes. Admittedly, Batman believed he was saving Rachel, but the Joker switched Harvey and Rachel's locations round.
Combined with a hostage situation in Swordfish. The bad guy has strapped the hostages with explosives that will go off if they get too far away from him. Two police officers who are Too Dumb to Live manage to grab one of the hostages and drag her away from the scene while she is fighting to get back inside. She blows up.
The entire point of The Professionals (so much so that merely listing the movie under this trope is a spoiler; maybe that's why it wasn't here before?)
Subversion: In Alan Dean Foster's Journey of the Catechist trilogy, Etjole Ehomba promises a dying man that he will rescue the beautiful Visioness Themaril, who has been kidnapped by the sorcerer/warlord Hymneth the Possessed, and return her to her home city. After many adventures, he and his companions storm Hymneth's fortress to discover that the Visoness has decided to stay, believing that her influence can make him less evil. Etjole proceeds to bring her home by force. As soon as they arrive, and he has fulfilled his promise, Etjole takes her right back to Hymneth.
In Terry Pratchett's The Light Fantastic, Cohen the Barbarian rescues a girl from a druidic sacrifice, only for the girl to complain that she had been waiting all her life to be a Virgin Sacrifice so she could get into paradise. What's more, Cohen's back goes as he tries to hoist the girl over his shoulder, and it ends up with the girl carrying him out of the stone circle.
And in the previous book, The Colour of Magic, Rincewind and Twoflower "rescue" Hrun the Barbarian from marrying the stunningly beautiful Liessa and, in the process, become King of the Wyrmberg.
To the point where she challenges the knights herself, suggests other captured princesses they could rescue instead, puts up a sign saying that the path to her dragon's cave is out, and eventually changing her title to "Chief Cook and Librarian" so that "saving" her sounds like a less glamorous rescue mission. She also horrifies one of the knights when she explains that the dragon is out borrowing a crepe pan. Explaining why the dragon is borrowing a crepe pan leads to the exclamation "You DO like it here!"
In Brewster's Millions and it's various adaptations, the attempts of concerned friends to either intervene in the protagonist's feverish spending of his newly inherited millions or wisely invest his money so that he'll save at least some of it tend only to frustrate the protagonist, since unknown to them he has to spend the original inheritance in order to gain an even bigger one.
In The Wheel of Time Siuan, against Egwene's explicit order, leads a raid to rescue her from the White Tower where she was being held captive as rebel Amyrlin. The order was given so the latter could undermine Elaida's authority by showing more efficiency and dignity as a leader even while being her captive, but this is almost ruined when the Tower Aes Sedai were suddenly reminded that she was the rebel leader.
In The Shattered World, Tahrynyar is so unwilling to be saved by Pandrogas, the sorcerer who'd been having an affair with his wife, that he deliberately averts his own Unwanted Rescue, letting go of the cliff's edge before Pandrogas can cast the spell to propel him to safety.
The medieval cronicle of the Danes, Gesta Danorum by Saxo Grammaticus, tells the story of Starkad who after having slain nine brothers in single combat angrily refused the aid of three passers-by he considered dishonourable, although his guts was hanging out of his belly. The rest of his story is pretty much like that as well.
The Rescue of Omar Ganski: The police knew Ganski was innocent, and were keeping him in a nice hotel room while they tracked the real killer's mafia connections, until Ganski's friends blew the cover.
In the classic Scottish novel The Merry Muses, a tourist from England forcibly rescues a Scotsman who's about to commit suicide. The Scotsman sues him for assault. And wins, because one notable difference between Scots law and English law is that under Scots law, committing suicide is legal.
In the Vorkosigan Saga novel Shards of Honor, Cordelia's crew turns up to rescue her from the Barrayarans, who have a reputation for brutality. But not only have they been treating Cordelia extremely well, but the rescuers also unwittingly reignite a (politically motivated, undeserved) mutiny the Barrayaran commander has just finished suppressing. Cordelia has to help defeat the mutineers all over again before she is willing to leave.
Live Action TV
In the Blackadder Goes Forth episode "Private Plane", Blackadder and Baldrick have been shot down over German territory and imprisoned by Baron von Richthofen who plans to give them "a fate worse than a fate worse than death"... being sent to Germany to teach young girls Home Economics. Naturally Blackadder is thrilled at the idea of leaving the trenches and the pointless war for good... until Lord Flasheart arrives to rescue him.
When Blackadder attempts to stall the rescue, Flashheart works out his game and forces them to come with him. (Though he makes it up to him slightly by headbutting Darling)
At the start of Buffy the Vampire Slayer's sixth season, Buffy is "saved" from hell by her friends. Problem is, she wasn't in hell but in heaven and was content that way.
In one episode of The Drew Carey Show, friends and relatives worry over the fate of comatose Drew and come close to pulling the plug on him if he doesn't recover because he requested that of his brother—but in reality he's having the time of his life with a giant party inside his head. Complete with his brother saying "I can't imagine what kind of hell he's in right now" followed immediately by a cut to him enjoying himself.
On LOST, Kate leads a rescue attempt to recover Jack, even though he's told her not to come back to the Others' campground. When she manages to sneak in, he tells her to get out, because what Kate doesn't know is that Jack is scheduled to leave the island the next morning.
Stargate SG-1, season six episode "The Other Guys": a pair of scientists save the team from capture... but in reality the team let themselves be captured so they could get in touch with a mole in the enemy army, and the scientists have all but ruined the plan. That is, until the mole is caught, so the team now actually needs rescuing.
Done hilariously on Charmed. When Phoebe and Piper turn up, Prue and her naked 'kidnapper' are making out, after having enjoyed a night together. No one's very thrilled.
In the Torchwood episode "Combat", Owen Harper is sent undercover to infiltrate an undercover fight club for men with too much money and too little sense of purpose whose main event involves seeing who can last the longest in a cage with a captured Weevil. After he's forced into the cage at gunpoint, the rest of his team bursts in guns a-blazing, shuts down the ring, and pulls him out. In the hospital afterward with his injuries, he explains that he didn't want saving- somehow, his time in the cage gave him a sense of peace he had never felt before. This isn't explained further, but he might just be suicidal.
Happened all the time on Robin Hood with Damsel Scrappy Kate, who (for whatever reason) just didn't seem to like it when the outlaws saved her life. By the fifth or sixth time, the audience was begging the outlaws to simply let natural selection do its job.
In the Doctor Who original series story "The Web of Fear", the Doctor submits to a plan which allows the Intelligence to drain his mind. His companions try to stop him and he fights them off. It turns out that he was not fighting them because he was controlled; rather, he had sabotaged the machine so that he would drain the Intelligence instead and his companions, by rescuing him, had allowed the Big Bad to get away.
In "The Night of the Doctor"Cass prefers death to rescue by the Doctor, because the Time War has so ravaged the universe that she considers the Time Lords no better than the Daleks.
Buster/Kim: Torture me all you want, Demonica, I'll never crack! Demonica/Jenny: Oh, but you will. Malicia/Megan: By the time we're through with you, you'll be begging to tell us everything you know. Demonica/Jenny: You'll be our puppet. Malicia/Megan:(stroking finger up and down his chest) Our slave. Buster/Kim:(enthusiastically) Great! You're doing great! (Tom Paris [playing the hero Captain Proton] bursts into the room waving a raygun) Proton/Paris: You're done for, Demonica! Malicia/Megan: Malicia! She's Demonica. Proton/Paris: Whatever. You two are going to jail for a very long time. Buster/Kim: I've got everything under control, Proton! Shouldn't you be getting back to Headquarters?
A 'misunderstanding' example in the third season Castle episode" One Life to Lose", where Castle believes his mother is being threatened with a knife by the man he believes is the murderer. When he and Beckett burst in on them, though, it turns out the knife the suspect was holding was only a plastic prop, and they were acting out a scene. (Castle's mother picked out a suitable apology in a catalog later that night.
In Saving Hope, Dr. Goran's first surgery at the titular Hope Zion hospital involves doing an experimental procedure that could (and ultimately does) save the patients arm, instead of amputating it like the patient wanted. Dr. Goran tries to talk the patient out of his survivor's guilt (he was injured in war) so he won't feel like he needs to be punished by losing his arm but is unsuccessful and the patient ungratefully sues the hospital (and wins.)
In season two of True Blood, Sookie and Eric try to rescue Eric's maker Godric from the Fellowship of the Sun. It turns out he was there on purpose, and wanted to die.
In the Modesty Blaise arc "The Vanishing Dollybirds'', Modesty and Willy set out to break a white slavery ring. However, at the end, it turns out that the girl they originally set out to rescue is perfectly happy as a member of the sheik's harem.
Variation in The Legend of Zelda: Ocarina of Time: Inside Jabu Jabu's belly, Ruto is more concerned with retrieving the Zora's Sapphire than with being rescued, and is more than a little stuck up about the whole thing.
In Reset Generation, players are defeated when their princess is "rescued" by another player. Since the princesses are aware of this fact, all of the rescues are unwanted and they say lines like the one at the top of this page when grabbed.
Many an MMORPG newbie has tried to pull a Big Damn Heroes moment, only to be berated for kill stealing. Turns out that when Death Is a Slap on the Wrist, people would rather lose their lives than have to spend more time on that trophy-collection quest...
In Knights of the Old Republic 2, you have to save Vrook from a group of mercenaries who are planning to cash in on a Jedi bounty. However after youw in, Vrook reveals that he got himself caught on purpose so that he could track down the person who had put the bounty out in the first place. To make matters worse, your actions have made the rest of the mercs desperate and they proceed to attack the settlers.
Played with beautifully in Braid. It turns out that the princess in the last level is actually running away from the main character.
Happens in Ratchet & Clank Future: A Crack In Time when Ratchet goes to save Azimuth from Lord Vorselon. It's apparently because he'd rather Ratchet go on to find the Great Clock by himself, rather than waste time to save an old Lombax. Azimuth's rescue did kind of bite Ratchet and almost the whole universe in the ass later, though.
Final Fantasy X: Two times, Yuna is left alone with Seymour. Both times, she has a hidden agenda and wants the others far away, so she can carry out her plan without interference. Both times, the others storm in and try to save her before she can enact her plan, and the second time, end up a liability, as their lives are used as leverage against her.
One Nodwick comic strip (based on a Dungeons & Dragons adventure in Dungeon magazine) involves the heroes rescuing a knight who gave himself up as a hostage/sacrifice to a dragon, leading him to berate them for putting the lives of thousands at risk. "Hey! He made Piffany cry! Get him!"
Serious example: Mo and Sojueilo's squad free Thomil's in Juathuur, depriving them of the fastest way to reach the villain palace.
One What's New? with Phil and Dixie mentions a tribe of amazons who kidnap men for sex. The kidnapped men fight like tigers against any attempts to free them.
lonelygirl15 has done it a few times, as the heroes rescue girls whose blood is "trait positive" to keep them from being used in a mysterious ceremony which will result in their death. These girls tend to have no idea they have anything to worry about and are very hostile to their rescuers until they either escape or are convinced. This is subverted when one girl actually turns out to be trait negative, meaning the heroes' actions weren't even an unwilling rescue but a plain and simple kidnapping.
Everyman HYBRID: The boys break "Damsel" out of the institution (with Jeff tackling a security guard in the process), and have no idea why she's angry.
We figured you'd be happy!
No, I'm - I would be, I'd be fucking stoked if they weren't releasing me today.
In Red vs. Blue, Churchnote , Epsilon-Church, from the memory unit, by Carolina.
Danny Phantom had Danny and Tucker attempting to rescue Sam from the clutches of an evil ghost prince who intended to marry her. Neither of them realized that she was this close to saving her own ass until it was too late—the situation became much, much worse.
An episode of Codename: Kids Next Door features Numbah 1 infiltrating a college where they remove kids' brains. He is subsequently captured but it turns out that the villain made up the "removing brains" thing to lure Numbah 1 (who doesn't get Brain Freeze) there so he could have a test subject for his perfect snow cone machine. Numbah 1 has no objections. His team soon bust in to rescue him, getting him horribly hurt in the process, while he begs to be taken back.
He never got to tell the man it was the perfect snow cone formula he wanted to make, the minute he finished it, after the man had been working on it for months but had highly sensitive teeth and gums and got brain freeze every time he tried his creations.
The Looney Tunes short Bear Feat, featuring Chuck Jones' Three Bears characters, ends with Pa - fed up with his idiotic wife and son - trying to commit suicide by jumping off a cliff. "I'm going to be free! Free at last!" he gleefully shouts as he plummets...but Junior shows up with a bucket of water and catches him at the last minute, earning a punch in the mouth for his efforts.
A "peaceful resolution ruined" example occurs in the episode of Aladdin The Series named "The Garden of Evil". The plant-like sorcerer Arbutus kidnaps princess Jasmin, but her kind and caring demeanor almost manages to alleviate his hatred to humans. Unfortunately, just before his oncoming reformation, Aladdin storms his castle.
In an episode of Batman The Brave And The Bold, Bats pulls Save the Villain against Joker, who'd been betrayed by the washed-up Golden Age supervillain he'd brought out of retirement. Joker is quite displeased, and says that he'd ruined his best joke ever - if the Weeper had killed Joker, he'd have "claimed his destiny," going from washed up lame bad guy to the king of crime. It sort of echoes movie Joker not wanting to be saved because he'd have made Batman break his code - even a Lighter and Softer Joker cares more about his game than even his own life.
Subverted in Johnny Bravo episode "Bikini Space Planet", where a bunch of beautiful alien girls abducted Johnny and he was rather enjoying it. Pops and Carl spent most of the episode developing a device to bring him back. All of their effort was for naught, since the girls ended up sending him back anyway but Pops and Carl were under the impression Johnny's return was their doing.
In another episode, Johnny is sent to a women's prison by mistake, and it's full of women so desperate for a guy that they're even willing to date him. When Bunny and Susie prove his innocence, he's literally dragged from the prison kicking and screaming.
In an episode of Teen Titans, Cyborg is accidentally sent back in time and befriends some medieval villagers. He agrees to help them defend their town against invading monsters, but gets brought back to the present by Raven the moment the battle begins. As soon as he arrives home, the first thing he does is yell at the team to send him back. He feels better, though, once he sees a history book and learns that the villagers won the battle.
In the Classic Disney Short "Mickey's Fire Brigade", Mickey, Donald and Goofy are firefighters trying to put out a burning building. Clarabelle Cow is inside taking a bath, unaware that there is a fire, so when the trio try to rescue her she mistakes them for peeping toms and hits them with her brush.
In Jimmy Two-Shoes, Heloise finally has Jimmy under the effects of a love sweater, and the two are about to kiss. Unfortunately, she also has Beezy under the effects of a fear sweater, who promptly "rescues" him.
In "Eye Spy" on PB&J Otter, Flick Duck is worried that everyone will think he's geeky if they see him wearing his new glasses. He has a fantasy sequence in which he is a superhero named "Glasses Boy" and Peanut, Baby Butter and Jelly refuse a rescue from him— they want to be rescued by a "real superhero."
The Amazing Chan and the Chan Clan episode "To Catch A Pitcher" has thugs kidnapping a star baseball pitcher, whom the Chan Clan rescues. But the guy isn't the star pitcher—he's a duplicate planted while the real star was in hiding, and the Clan's rescue of him may have spoiled the cover.
The Looney Tunes Show: In "Itsy Bitsy Gopher", Bugs dashes into a house full of poison gas to rescue what he thinks is Gossamer's pet spider. However, it turns out not to be Gossamer's pet, but instead a deadly African sand spider which bites him in the face.
During World War II the 101st Airborne was surrounded by the Germans at Bastogne and stuck in the bitter cold of Winter with ammo and food slowly dwindling. General Patton and his Army division came blazing through the area and reinforced the 101st Airborne, in the eyes of the American Military community at large Patton had rescued the Airborne. After the ordeal a good deal of the 101st Airborne refused to accept that General Patton "rescued" them saying that they were never in any need of rescuing.
Despite the commonly considered Refuge in Audacity "Nuts" comment by the commanding American general. In reality the surrounding division that was actually outnumbered and was more under supplied than the unit they were besieging. The real Refuge in Audacity in that fight was by the surrounding division asking for surrender. So in a sense they were right, just not in the sense they thought at the time.