Mazinger Z: Kouji Kabuto did this -outofall people!- in episode 7. After mobs of people expressed their displeasure in having their hometown leveled by Humongous Mecha battles by harassing him, and after a quarrel with Sayaka, Kouji decided that since nobody wanted him fighting, he would stay in home. Of course, it did not last long.
Tetsuya also did it in the last episode of Great Mazinger. He was so jealous of Kouji he refused to sortie in Great Mazinger to help him when he was struggling.
It's not stated outright but based on Shinji's Sync Ratio shooting up to an 'impossible' 400%, plus the next episode revealing that Shinji's body has vanished and his soul has been absorbed by the Eva in essentially the same way as his mother's was, it seems it really was Shinji's will driving the Eva this time.
Way less debatable in Rebuild, where even Mari fails to take out Zeruel and Shinji pwns it himself by directly accessing Eva01s god-like powers without any berserk whatsoever.
An inversion of this trope happens in a sports shounen manga, Fight No Akatsuki (Akatsuki's Fight), in that the leave-taking is actually an admirable and sensible thing. Two best friends, Akatsuki and Kiyo, are on opposite teams. The coach of the Opposing Sports Team orders his players to injure Akatsuki so bad that he can't play anymore. Kiyo hurls a basketball at the jerk's head, says nuts to that, and sits the game out rather than be a part of that. After they fail to stop Akatsuki, Kiyo returns to the game to play against his best friend fairly.
Chang Wufei spends an entire episode of Mobile Suit Gundam Wing doing this after failing to kill Treize; it takes words of encouragement from future Team Mom Sally Po, and the deaths of her mercenary friends, to snap him out of his funk.
This happened as early as the original Mobile Suit Gundam - Amuro heard Bright and Mirai talking about how dependent they are on Amuro being Gundam's pilot and, tired of being treated like he was, takes the Gundam and runs off. He does come back an episode or two later and they toss him in the brig for it.
It also happens in Mobile Suit Gundam 0083: Stardust Memory. After wrecking the GP-01 before it could be modified for space combat, a distraught Kou Uraki disappears after one of his co-pilots drunkenly reads him the riot act. He disappears for awhile, befriending a Zeon pilot in the process before returning to duty.
One Piece had a somewhat subverted version of this trope play out over an entire two-year long story arc. Usopp protests when the crew decide to junk their broken-down old ship in favor of a shiny new one, as the ship had been given to them by his girl back home, and was practically one of the True Companions. Told to get over it by Luffy (in a rare scene where he actually issues an order as captain) Usopp chooses to leave the crew instead. Later, our heroes find themselves in huge trouble, so Usopp returns to help out, but, unwilling to face his former comrades, he shows up in an incredibly obvious disguise (which still manages to fool two of the more gullible crewmembers.) Despite helping save the day, he is still not asked back on the crew, (even though everyone really wanted him back) since he went against a direct order from his captain. Only when he apologizes without provocation (and, as it happened, does so very loudly) do our heroes welcome him back.
This example even adds the second part of this trope, where the character's specific talents become needed. The story was a Rescue Arc, with Robin, the crewmember they were trying to rescue, being carried away by the Non-Action Big Bad. By the time anyone is in a position to stop him, he's too far away for anyone to do so, with the Big Bad having a significant head start over even the guy closest to him. Fortunately, being a sniper, Usopp was able to slow him down from a distance, buying the previously mentioned closest guy time to catch up and administer a more direct rescue.
In Code Geass, Lelouch has a few moments like this after his various Trauma Conga Lines. The most unfortunately timed one is in R2 episode 19, where because he's in his chambers and not responding to calls after his most recent and crushing one, Schneizel is able to almost completely demolish Lelouch's already-tenuous credibility as Zero and reveal his secret identity and mind control power.
Sailor Mercury is prone to the more benevolent versions of the standard plot; she starts as the only Senshi without offensive abilities and is too nice to storm off. Instead, she's offered a chance to study abroad and further her goals of becoming a doctor, which will remove her from the Senshi. She's about to take it, but changed her mind at the last moment so returns in time to get her mid-season power upgrade (which finally makes her more action-geared) and rescue the rest of the team from a monster only weak to ice, and she returns to the fold. Later in the season, she's attacked by a monster that causes paranoia and self doubt, and she hallucinates that everything everyone says to her is derisive and mean. Eventually, her faith that her friends would never say such horrible things allows her to break the spell and come back to everyone.
Sailor Venus also has an episode where she decides to leave the Sailor Senshi — not because she's upset, but because she wants time off from saving the world so she can rejoin the volleyball league she was forced to quit as well as get a boyfriend. Who should show up but a Monster of the Week with volleyball-related powers attacking Venus's love interest. After defeating the enemy, she then decides to go back to being a Sailor Senshi, possibly after learning that said love interest already has a girlfriend.
In YuYu Hakusho's Chapter Black Saga, Hiei, whose helping the heroes had until this point been reluctant, refuses to help them after hearing about the plan to open a portal to the Demon World, which would enable him, a B+ class demon to return there. He returns to help Yusuke against Kaname "Sniper" Hagiri, and is persuaded to help after being offered the Chapter Blacktape.
Brad/Ballad in Zoids does this in one of the beginning episodes, refusing to fight the Backdraft Group because he won't get paid for it. Of course, he comes in at the last minute and saves everyone... because Dr. Toros offered him Bit's next few paychecks.
Saiyuki has one of these for every one of the Sanzo party apart from Goku (although Hakkai's is anime-only), which results in the rest of them going "fine see if we care" and "we can manage just fine without...."
When Gojyo stays behind to go after Kami-sama the others eventually go back, the reason they give is he's caused so much trouble they have to go beat him up. Which they do once they get there (arriving at just the right time) however Gojyo realises he needs them; in a slight subversion, however, it is him who manages to save all of them when the building starts falling down.
In the anime Hakkai ignores all of the others for a while because he's waiting for them to apologize for not tidying up as they promised to (reload filler is odd sometimes) they say "we're not apologizing, we can manage without him" and try to (Hakkai does all the cooking and cleaning and has taken the credit card so...). He breaks when Goku can't stand it any more and comes and tells him how horrible it is and basically makes the other two apologize.
Sanzo's one lasts considerably longer than any other separation (they manage without him for longer, and he's more stubborn); he's gone off on his own private agenda for a bit.
The only time they admit they can't manage without a member is when Jeep goes missing (Hakkai says that it's worse than when Gojyo left, causing the latter to object that he shouldn't place below a car).
Occurs in Galaxy Angel when Ranpha has quit the group to get married and settle down. Meanwhile, the Angels are tasked to pilot a giant combining mecha to fight galaxy monsters. Every one of their attempts to make the mecha combine ends in an explosion. Milfeuille remarks that "It seems we're no good without Ranpha." Being Galaxy Angel, the trope is subverted when Ranpha arrives to save the day and the mecha still explodes.
Michael from We're Alive spent part of season 2 sulking in his room after Burt took over as leader of The Tower. He comes out of it by volunteering to find medical help for Saul and by the time he gets back he's ready to take back command.
The Fantastic Four was notorious for this happening, particularly with the Thing.
Again in Marvel, Namor was rejected by the Atlanteans and later he rejected them. It took the god Neptune giving Namor his trident to change Namor's mind.
Subverted in Justice League Elite by Major Disaster who suffers a breakdown after his alcoholism gets a teammate killed. When the call comes for him to return, he refuses in an attempt to stay away from the things that drove him to drink in the first place. Vera Black decides to respect this rather than risk pushing him into a relapse. He does answer the call during Infinite Crisis, where he gets killed.
The Sentry from Marvel Comics tends to do this a lot. The main reason for this, of course, is that he is described as the world's most powerful hero and in all probability could solve any problems of other heroes nigh-instantly. In his first appearance in New Avengers, he effortlessly flies Carnage into space and rips him in half. When his evil counterpart the Void emerges, it takes the entire New Avengers, the X-men and the Fantastic Four just to hold it off long enough for the Sentry to beat it in a battle in the center of the mind.
In Judge Dredd, during the First Robot War, Dredd leaves the Justice Department when Goodman refuses to have all the robots in Mega-City One decommissioned. Sure enough, the robots rebel, but Dredd comes back by the end of his retirement strip.
In Batman: No Man's Land, Batman himself pulls this after he fails to stop Congress from condemning Gotham City. An encounter with Talia al Ghul gets him to shape up and return to Gotham three months later.
Omega Supreme has lived in seclusion since the Golden Age of Cybertron, only nominally allying with Autobots and generally believing that the Cybertronian race may be beyond salvation. However, after being attacked during the events of Transformers: All Hail Megatron he returns to save the Autobots on Cybertron and begins to work more closely with the main Autobot army, even holding out hope that change is possible.
For most of Origin Story, Alex refuses the call. She's possibly the most powerful superhuman on Earth, and has the right attitude to be an effective force for good, but all she wants is to be left alone. Eventually, she comes around.
Films — Animated
Yet another non-combat version: In The Jungle Book Bagheera throws up his paws in desperation at Mowgli's continued rebellion, only to return when he gets in trouble again. He returns no less than three times: upon Mowgli's initial encounter with Baloo (which turns out to be a false alarm), when Mowgli gets kidnapped by monkeys, and when Mowgli runs away from Baloo.
Troy. "We stay until Agamemnon groans to have Achilles back!"
Bonus points for him being in an actual tent as he said that.
Star Wars: A New Hope - As soon as Han Solo gets the money for doing what he was hired to do, he jumps ship, claiming that he's Not in This for Your Revolution. Of course, even people who haven't seen the movie knows what happens next: "You're all clear, kid! Let's blow this thing and go home!"
Then he does it again at the beginning of The Empire Strikes Back, though not directly onscreen. He also doesn't spend long running from bounty hunters before he discovers that Luke has gone missing and he pops back out again. The phrasing implies that both he and the Rebellion fully intends the tenting to be temporary in the Empire case — it's not that Han Solo wants to leave, it's just that he's living under a death sentence while his debt to Jabba goes unpaid.
Parodied somewhat in Team America: World Police, where Gary is accused of this despite the fact that his abilities would have been obviously useless— though, of course, they eventually do need an actor for the final mission.
Lancelot becomes a partially insane vagrant in the movie Excalibur who blames the king for bringing a pestilence upon the land. At the climatic battle, he returns to fight by the king's side.
In X-Men: Days of Future Past, '70s Xavier gives up on his powers and his role as the leader of mutants, and refuses to cooperate with Wolverine; without his aid, the entire venture is impossible. He's got more justified reasons than in most examples of the trope, but still.
A non-combat variant of this occurs in This Is Spinal Tap. Due to an increasing series of setbacks and personality conflicts, Nigel Tufnel stomps off in the middle of a show (which is going very badly), effectively quitting the band. The band's fortunes continue to get worse, as their venues and audiences get smaller, and they're forced to cut all of Nigel's songs (eliminating the bulk of their set). Finally, in the last ever performance of what's left of Spinal Tap, Nigel returns with an offer to reunite for a Japanese tour supporting their latest album. Rejected at first, he's invited back, as an expression of the The Power of Rock/The Power of Friendship.
Named for the famous incident in Homer's Iliad, which fits the formula almost perfectly, with an added touch. Agamemnon tries to coax Achilles back by meeting the demands he originally made before the new threat, but Achilles now refuses them. Also, in stark contrast to modern TV examples, Achilles does not learn An Aesop about teamwork or friendship. He re-enters battle out of pure blood rage, after his best friendcousin Patroclus kicks the bucket, and winds up forming an Odd Friendship with the enemy king instead of with Agamemnon.
The Achilles situation is exactly mirrored in the final book of the Percy Jackson and the Olympians series: Clarisse, daughter of Ares, refuses to let any of her siblings join the fight because they won a prize in battle that got taken away. Even after they get it back, she won't fight in the war. Eventually Clarisse's new best friend, Silena, daughter of Aphrodite, steals her armor, leads the rest of Ares's children into battle, and gets killed in the fight. Clarisse then rejoins the war, just like Achilles.
Well, given that the entire series is a big Shout-Out to Classical Mythology, and just about every event is some modernized version of an ancient Greek myth, you knew this one had to turn up sooner or later. Percy even gets the same powers as Achilles in said book by bathing in the river Styx. And Achilles' shade makes an appearance to try to talk him out of it.
In the same book, Hades refuses to help his fellow Olympians against Kronos.
The Star Wars Expanded Universe featured Garm Bel Iblis, a founder of the Rebellion who left when he felt it was risking becoming a dictatorship, feeling that replacing the Emperor with an Empress wouldn't be an improvement. After realizing his folly, he returns but refuses to take command of the fleet, even while they're being attacked, by an enemy commander that only he is skilled enough to match. He finally gives in after speaking with Mon Mothma.
Played with in Tad Williams' Otherland series. In a memorable sequence, the protagonists find themselves in a computer simulated version of the actual Trojan War, filling the shoes of many of that story's heroes. Orlando is Achilles, but in a subversion, the reason he can't come out to fight is because he's genuinely too ill. The NPCs still treat him according to the story line, though, forcing Sam (as Patroclus) to don Achilles' armor and confront Hector. In trying to rescue her, the protagonists inadvertently trigger Hector's death and the subsequent sacking of Troy.
The entire premise of Atlas Shrugged is that the people really important to civilization decide that it's no longer their job to let their skills benefit if they themselves cannot also enjoy the fruits of their labor. Of course, here it's portrayed as the right thing to do.
An interesting inversion occurs in Aztec, where the protagonist, Mixtli, tends to leave the city and go wandering about whenever he suffers a Heroic BSOD, rather than stay at home. It has the same effect on his friends and companions, though.
In Septimus Heap, Septimus runs off from the Quarantine laid around the Palace in a fit of anger after having been excluded from the Quarantine Spell.
Don Quixote: Being present in a lot of Chivalric Romance books (Amadis of Gaul, Beltenebros and Orlando did it), this trope is parodied by Don Quixote: When he is at the Sierra Morena forest, he invokes this trope by sending Sancho with a letter to Dulcinea (his imaginary love interest) explaining her that he will be in the forest until she forgives himů Even when don Quixote has not made anything against her. This madness will force the Curate and the Barber to ask Dorotea to pretend to be a princess and ask Don Quixote a favour to get him out of the forest.
In Animorphs, team leader Jake pulls this towards the end of the series. Though it's more justified than most examples, seeing as how he was grieving over his failure to keep his parents from getting infested.
"Ye see it easily enough in a spoiled child that would sooner miss its play and its supper than say it was sorry and be friends. Ye call it the Sulks. But in adult life it has a hundred fine names —Achilles' wrath and Coriolanus' grandeur, Revenge and Injured Merit and Self-Respect and Tragic Greatness and Proper Pride."
Sammael spends centuries alone in a tower because he gets fed up with the eloim and their ideas of how to live on Earth in Burying the Shadow. Gimel finally manages to bring him back in their hour of need after things nearly go to hell, but it's not as epic as everyone expects.
Live Action TV
A rare non-combat example: the 1980s children's puppet show The Letter People. In an early episode, Miss A gets into a fight with the other letters and quits. Since Miss A was the only vowel in the cast at this point, nobody can form a word without her and they have to beg her to come back. (Since she was also the only female letter introduced at this point, this may have been a sly way to teach feminism to the target audience.)
In Angel, Wesley left, not entirely of his own volition (he was heavily injured), after during Season 3 and his mistake with Connor, followed by about a season of intermittent contact with the team, during which they sometimes sorely missed his talent. He just sort of drifted back in about mid-season 4 with the whole Cordy crisis.
The premiere of the second season. In "When She Was Bad" Buffy comes back from her summer in L.A. still steaming with issues from being killed for a minute in the Season One finale. When the Master's men steal the Master's bones with the intent to resurrect him, Buffy explodes at Giles and blows off the Scooby Gang's attempts at consoling her. This lasts until Willow, Giles, Cordelia, and Miss Calender are captured by the vampires for the resurrection ritual. In this case, the prompt for her glorious return is less that she realizes that she's needed and more that it's brutally spelled out for her by Xander, who basically gives her an "As a result of this mess I'm completely over indulging your self-pity; get over yourself and do what you should have done in the first place" speech.
Buffy getting deposed by her own pupils in Season 7, who install Faith as their new leader. One episode and bomb explosion later, and everyone goes crawling back to blondie.
Not quite an example, but certainly an honorable mention: In Star Trek: The Next Generation episode "Peak Performance", Data loses a game of strategy that he expected to win. Because of it, he loses confidence in his abilities and stays in his quarters, trying to determine what is wrong with his programming. Several crewmembers try to get him out of it and back on the bridge; Dr. Pulaski at one point marches straight into his quarters and demands, "How long are you going to be sulking like Achilles in His Tent?" He's convinced that he's not unreliable and takes his place on the bridge in time to assist in a sudden crisis and formulate the plan to save the crew.
In Star Trek: Voyager, Janeway does this in the episode "Night". The ship has entered a void, no stars, no planets, no gases, absolutely nothing. They slowly go stir crazy and She falls into despair and remains in her quarters, blaming herself for stranding them in the Delta Quadrant. Chakotay tries to get her out of it citing the crew needs their captain, but she ignores him. An alien attack however, brings her back to protect her crew.
In Robin Hood: Robin overpowers Guy and ties him to a tree after realizing that he is man behind the attempted assassination of King Richard. He gets so wound up that he nearly resorts to torture and refuses to listen to his men who feel that it's more important to stage a rescue mission to save a fellow team-mate that's been captured. After several failed attempts, during which Robin just sits under a tree, the outlaws return unvictorious and it takes Marian to snap Robin out of it and suggest a hostage trade.
In season 5 of Babylon 5, Garibaldi is assigned to monitor intelligence reports and coordinate the peacekeeping forces to prevent a war from flaring up. While he's busy drowing his sorrows, the war escalates and the peacekeeping forces are unable to regain control before Centauri Prime is bombarded from orbit.
In Between the Lions, Click (the computer mouse) is jealous of Lionel and Leona making a fanclub for the little brown mouse (in the Lion and the Mouse), due to them thinking of her (the mouse) as a hero, and decides to leave. But then she finds out that Cleo is in a trap in the book and needs to be rescued, and returns.
Happens in Glee in the episode Sectionals, when Finn abandons New Directions after learning that Quinn's baby isn't his and that the rest of the club had helped her to keep the secret. Naturally, he shows up to sectionals right after their two competitors finish performing (all of New Directions' intended songs) with new pieces prepared and ready to go.
In the M*A*S*H episode "The Late Captain Pierce", a clerical error leads to Hawkeye being declared deceased. Tired of the war, and tired of attempting to get the mistake corrected by the Army bureaucracy (and to contact his father back home to let him know he's okay), he takes off with the ambulance that's there to collect his "corpse", just when new casualties arrive. After the ambulance leaves the camp, it stops, and Hawkeye walks back to the 4077.
A very temporary incident happens in Power Rangers in Space. Carlos loses confidence in himself and leaves the team after a Monster of the Week uses his teleportation to swap himself with one of the other Rangers he was grappling with, causing Carlos to harm them. Encountering Adam and a second chance at the incident gives Carlos the strength to fight on and return to the team.
The 2012 Doctor Who Christmas special sees the Doctor hiding out in Victorian London with the TARDIS parked on an artificial cloud, claiming to have given up saving the world after being separated from Amy and Rory.
Later revealed that the Eighth Doctor was this to the Time War, only getting involved in the last minutes before his regeneration, and only when he passed the Despair Event Horizon about said war and realized it had to end ASAP.
Alias: When Dixon learns the truth about SD-6, and that Sydney's been a double-agent for the CIA for a while, he feels incredibly betrayed. Although he's offered a good position with the CIA, he quits entirely and wants nothing more to do with Sydney ever, nor the intelligence world, nor the team he used to be a part of (who have all joined the CIA). A dangerous mission crops up that desperately needs Dixon's personal knowledge but he refuses to get involved, so Sydney takes his place. When she's captured because of information she lacked, Dixon rushes in to save her life, rebuilds his relationship with her and joins the CIA.
Ilya Muromets from Russian mythology. In one legend, his break with Prince Vladimir seems to be forever, but actually only lasts until a new threat for their Motherland appears. Reluctant Ilya agrees to go fighting, "not for the Prince, but for the sake of common Russian people".
Actually, a recurring trope in Russian mythology. A number of heroes acted in a similar way. A similar line is attributed to Alexander Nevsky.
This trope pretty much defines Sting's character in WCW through the entire year of 1997. Hell, we might as well call this trope Sting In The Rafters.
Falco from Star Fox did this in Adventures, and in one of the endings in Command.
Susano, the Fake Ultimate Hero of Ōkami, does this when he finally admits, to the villagers and himself, that the Orochi of legend was real and he has released it. It takes his girlfriend, Kushi, to shake him out of it, and even then she is nearly eaten by Orochi herself.
In The Order of the Stick, Roy decides not to help the rest of the team rescue Elan, because Elan is too useless to be worth the risk. He changes his mind the following night, after he realizes how much of an asshole he's being.
More that he realizes he is being untrue to himself by abandoning Elan - his whole reason for becoming a fighter and an adventurer was to help others. When Roy dies (he gets better), he learns that had he not gone back, he'd have ended up in a rather worse afterlife. Though it also helped that in a later adventure he acted more promptly to save Elan's life.
Referenced in one Penny Arcade comic in which Gabe asks his Guildmaster permission to try a different MMO. The Guildmaster's response is to purposefully do something that requires Gabe's character.
Gabe: But...that is suicide! Kiko: Is it, druid? I call it murder.
In Erfworld, despite his defense of Gobwin Knob being an overwhelming success, Parson distances himself from military strategy at the end of Book 1 after seeing the enormous death toll his command caused for both sides. He spends the inter-book updates and the first third of Book 2 managing the city, which in Erfworld terms means just walking around symbolic buildings to increase their efficiency. He believes this will not cause any moral consequences. Then suddenly Ansom, who replaced him as Chief Warlord, falls into a trap at the Siege of Spacerock, Parson is reappointed Chief Warlord against his will, and has to once again save his side from near-certain defeat. This time, however, he decides to join his subordinates at the battlefield and face possible death with them, instead of strategizing from the safety of the war room.
In Series 2 of Phaeton Sierra does this when she sees the petrified orphans.
One of the very first Thomas the Tank Engine episodes written featured Henry trying this in "The Sad Story of Henry". In this case the episode ended with Henry being locked in the "tent" he sulks in for "Always and Always and Always." and it wasn't until the following episode that Henry got to make up for his wrong-doings and save the day.
In "Trouble in the Shed" Henry tries it again, along with Gordon and James and once again, it backfires. The Fat Controller shuts them up and gets Thomas and Edward to run the line.
Kim Possible: Ron quits when he thinks Kim is jealous of his new success at Bueno Nacho. Kim thinks she can do without the goofy sidekick, but it turns out he's vital. Him or his naked mole rat?
Teen Titans: Cyborg quits after a fight with Robin, then returns just in time to save Robin, and then they save everyone else.
A couple of times in Theodore Tugboat. In "Guysborough's Garbage" the eponymous Guysborough refuses to collect garbage, resulting in the Big Harbour becoming a big mess. A visiting ship, to whom cleanliness is Serious Business insists on leaving the harbour.
There was also one time when Hank, feeling that no one respected him because of his short name, changed his name to Henry. After a big mix up, a large barge goes out of control and speeds through the harbour. Hank is the only one fast enough to catch the barge but he ignores their pleas for help until Theodore addresses him as Henry.
W.I.T.C.H.: Cornelia quits when the team fails to protect her best friend, Elyon Brown, from the bad guys. Without the full team, everybody else's powers are weakened (which strangely didn't happen the last time the girls had to send a partial team), and new monsters attack who Cornelia's powers would have been perfect for. She inevitably snaps out of her funk in time to save everybody. This turned out to be a turning point, giving Cornelia real Character Development for the first time.
In an episode of Recess, Gus refuses to take sides in a dodgeball fight, despite being a dodgeball virtuoso at one of his older schools. Upon seeing a younger student getting clobbered, however, he enters rage mode and proceeds to wipe out the opposing team single-handedly.
A variation of this is shown in Beast Wars, where Tigatron does this after he accidentally kills (a non-Transformer) tiger friendhis mate in a firefight, and only returns after he realizes the bad guys aren't going to stop destroying if he does nothing. Somewhat unique in the fact that the teammate that attempts to coerce him back into the fray is a battle-hungry warrior who attempts to strong-arm him under threat of death, which certainly didn't help matters any.
Captain Planet had at least two episodes with Ma-Ti angsting, trying to quit the team and having to come back to save the day. Hell, Kwame tried to quit once in the middle of an Heroic BSOD, and he was the de facto leader of the team. There was also a two-parter episode where Wheeler tries to change history so that he never became a Planeteer, only to travel forward in time and discover the world was destroyed by global warming because everyone was DOOMED without him.
This happened to The Tick in "The Tick Vs. Arthur's Bank Account". Handy the Hand Puppet even points out the allusion.
Handy: Even now he sulks like Achilles in his tent! (beat) Achilles? The Iliad? It's Homer?! Read a book!
The entire TMNT movie could be a variation on this theme. Leonardo has stayed in South America for a year after his training was supposed to be over. While he's gone, Raphael develops some serious anger issues with his older brother, and sort of does the inverted Achilles in His Tent as the team falls apart: he goes out and fights crime solo as the Nightwatcher while his two younger brothers work menial jobs, watch television, and play video games. When Leo comes back, Raph is way too angry to reconcile with him, and keeps up his Nightwatcher act until Leo - literally - "unmasks" him. Leo and Raph duel, and Raph almost wins, but backs off when he realizes he's become angry enough to actually hurt (kill?) his own brother. As Raphael runs away, he hears Leo scream as the Big Bad and his Five-Bad Band capture him. He tries to go after Leo, but the bad guys get away. Raphael returns home, where Splinter gives him some Epiphany Therapy, after which he leads the other turtles (with some help) to storm the bad guys' tower and rescue Leo.
In the 2nd season of the 2012 series, April tells the Turtles she never wants to see them again after their blunder earlier on causes the Kraang's shipment of mutagen to get scattered all over New York and one of the canisters mutates her father into a monster bat.
The Simpsons had an episode where Marge buys an SUV, gets road rage, and has her license revoked. The next day, Homer's idiocy causes a breakout of rhinos at the zoo. Chief Wiggum immediately comes crawling back begging her to put her anger to good use, but Marge stubbornly refuses. That is until she looks at the TV and sees her family surrounded.
Family Guy lampooned this with the exterminators in season 2 ep 17. One of them, named Logan, is having an emotional breakdown because his family was carried off by fire ants. But he shows up just in time to save his fellow exterminators from a flea infestation. Please note that instead of being "exterminators" with insecticides, they're basically a bunch of soldiers with guns and body armor. Also please not that the "Rescue" was shooting one single flea that was approaching three heavily armored men.
The Powerpuff Girls does this in one episode. Bubbles gets humongous glasses and is teased by her sisters until she flies away, sobbing. Turns out that they need to her to fight a giant ant, and while Blossom and Buttercup's heat vision isn't strong enough, Bubbles' sure is when it's magnified 10 fold by her glasses, killing the monster and saving the day.
Blossom goes through this in "Not So Awesome Blossom." Her confidence is shot after her strategy against Mojo Jojo's droid army causes collateral damage to the city. Blossom can't do anything right to the point where she runs away from home. Mojo uses this as a bargaining chip against her.
In one episode of Totally Spies!, Alex quits WOOHP, and is replaced by Britney. The former returns to action when the latter and the other spies are captured.
Regular Show features this in "Prankless" when Muscle Man quits pranking after nearly killing Pops. They need him back when a rival park restarts a prank war that Muscle Man succeeded in winning in the past.
This happens in Scooby-Doo! Mystery Incorporated with Fred Jones in the season 1 finale, after he discovers that Mayor Fred Jones Sr. was never his real dad, and stole him from Brad Chiles and Judy Reeves so that the original Mystery Incorporated would never go back into Crystal Cove. Fred quits the gang so that he can search for his biological parents, and leaves with the Wham Line.
Some people on message boards do this in an attempt to prove how indispensable they are. You've probably come by more than a few of those "Leaving the fandom, back in five minutes!" types. This is especially prominent in MMORPG message boards whenever a game takes a turn that a player does not like. Of course, many Free-2-Play games subvert this by usually saying "I quit" posts are not allowed and they are free to come back at any time.
And then there are people who fake their deaths and return as (often badly disguised) sock puppets to grieve and pile on the "posthumous" praise.
In the late days of People's Republic of Poland, after the introduction of martial law, many people in the media decided to quit their (well-paid jobs) as way of protest against the regime. Because of the scale it was an additional hit to the image of the government.