In Max Havelaar, the Governor-General of the Dutch East Indies fires the "troublesome" Havelaar, but offers him a new position in a remote district, where he can presumably cause less trouble (read: do less about the injustices suffered by the local peasants). An enraged Havelaar refuses.
Chigago PD's Special Investigations (SI) department in The Dresden Files. The division is nominally for handling "weird" stuff, some of which is actually magic. However, it also happens to be professional Siberia in CPD-politics-land. Dresden comments on this from time to time, mostly because these are some of the sharpest, and bravest (Loup-garu incident anyone?) agents in the police force, but they either pissed off their previous bosses, or some major politician. Probably both. Or Marcone.
To be sure, they don't universally land themselves there by being grossly competent and by contributing to civil order and such terrible things, but the ones who stick around tend to be this. (The rest quit out. Or die.) It also helps that they have an honest-to-goodness Wizard, Harrymotherf***ing Dresden.
Vince Graver quit when he found out he was voluntold, and has been doing significantly better for himself as a PI than Harry. Or anyone in SI, for the matter.
Waldo Butters, the coroner, found himself permanently assigned to the night shift after reporting a number of bodies pulled out of a burned-down building as "humanoid but non-human". The fact that the bodies were Red Court vampires didn't faze anyone higher up on the ladder because everyone knows there's no such thing as vampires.
Several examples involving "Camp Permafrost" — a cold-weather training camp at Lazkowski Base:
Miles Vorkosigan's father Aral explains to Miles that he was once CO of Lazkowski Base for about six months "During the period when my career was, so to speak, in political eclipse." When Miles asks him about his experiences Aral admits he was drunk most of the time.
In an earlier book we learned that Aral's first command after Camp Permafrost, the cruiser General Vorkraft, was nicknamed "Vorkosigan's Leper Colony" because of all of the New Meat, political unreliables, screw-ups and borderline psycho cases that were assigned to his command as punishment for him and for them. Not surprisingly this also results in an Reassignment Backfire because Vorkosigan epitomizes A Father to His Men.
Miles himself is an metaphorical example. His own assignment to Lazkowski Base in The Vor Game is a matter of paying his dues: having developed a reputation for treating his superiors as "cattle to be driven", his first assignment after graduation from the Imperial Academy is supposed to test his ability to work as a junior officer with ordinary soldiers and officers. When things blow up, his career in the regular Imperial Service is aborted — he's reassigned to ImpSec where, as far as (almost) everybody knows, he spends the next ten years as a glorified mailman.
Lt. Vormoncrief gets sent to Camp Permafrost in A Civil Campaign. Spreading phony murder accusations about an Imperial Auditor (who happens to be the Emperor's foster brother) because he's getting the girl you were after? Likely to really tick off the Emperor. Convincing people that the Emperor is too incompetent to keep peace in the capital, two weeks before his wedding? Reassignment to Antarctica, and lucky to be laundry officer when you get there.
Gregor ends up handing out several such assignments at the end of Captain Vorpatril's Alliance. After a major government agency's headquarters gets dropped into a manmade sinkhole up to its roof, it's tough to blame the Emperor, even if it was an accident.
In Ivan's case it is something of a subversion. Ivan and his wife are assigned to a minor consular post which they find was incompetently run, but not particularly bad. After Ivan streamlines the local system so it can run efficiently (and thus have no disturbances incompatible with his standards of sloth) he simply moves the entire consulate from the depressingly rainy capital to somewhere with a lovely tropical climate. When last we see him he is cuddling with his wife on the beach and sipping "girlie drinks".
Meanwhile, Simon Illyan is "encouraged" to go on a long vacation, in his case to Beta Colony with Lady Alys. They take full advantage of its hedonistic delights (such as The Orb).
In Harry Turtledove's Ruled Britannia, Lieutenant de Vega is constantly threatening his lazy servant with reassignment to Scotland until he gets some better blackmail.
The Timeline-191 series features recommendations along the lines of "heading up the Coast Guard in Nebraska" for officers who screw up badly enough. (Nebraska is landlocked.)
Played completely straight in Pocket in the Sea, but with a reasonable explanation as to why the characters have been reassigned to such an awful posting.
Lord Asriel in The Golden Compass is theoretically imprisoned at Svalbard, guarded by armored bears. However, since he's an influential nobleman, he's still got a house and a servant, along with books and a fully equipped laboratory, so it seems he's not so much in prison as exactly where he wants to be.
On the other end of the spectrum, there's one Captain Virar Needa, who was shunned for being related to the Star Destroyer captain from The Empire Strikes Back. He was reassigned to a drudge post babysitting an orbital satellite with a crew of maybe six. He explicitly mentions the post is as close to dead as you can get in the Imperial Navy without shots actually being fired (which is what happened to the rest of his family).
Early in Seven Days in May, a Pentagon communications officer blabs to the book's protagonist (a fellow officer) about a seemingly-innocuous bit of gambling by some high-ranking officers, neither of them knowing that it's actually a code related to a looming Military Coup. In a savvy moment, instead of a heavy-handed punishment detail, the coup-leader has the blabber shipped off to Hawai'i.
In The Malloreon, Belgarion manages to convince 'Zakath to do this instead of killing the guy. It was pretty easy, given that killing indiscriminately cost 'Zakath his wife and caused his breakdown when he learned she really was innocent.
In the legendarily bad Battlefield Earth, head Big Bad Turl is stuck on the backwater mining planet of Earth because he pissed off some of the wrong people back home.
In Brave New World, Bernard Marx is initially threatened with being reassigned to Iceland for being a nonconformist, but he manages to avoid this by presenting some skeletons from his superior's closet just when he's about to do this. In the end, both Bernard and his friend and fellow individualist Helmholtz Watson face being sent to "an island" by their highest superior; it's standard procedure to send people who start to think too much and rock the boat to various islands where they can hang out with each other and not bother anyone else. It can even be seen as a good thing for those people, as they can get away from the oppressive society and among people like themselves. Their friend John, who's grown outside the dystopian "civilised" society and can stand it even less, would actually like to go with them but isn't allowed.
In Catch-22 , ex-P.F.C Wintergreen deliberately causes this for himself by constantly going AWOL from the army. Every time he is caught and court marshalled, and sentenced to digging and then filling up holes in the middle of nowhere for a specified amount of time. He is wise enough to know that in World War 2 this is the safest thing he could be made to do, so continues to go AWOL.
In Away Boarders, a comedic novel by retired Admiral and Real Life badass Dan Gallery, the crew of a Navy landing craft stationed in the Mediterranean participates in certain events that, while they helped substantially defuse tension in the Middle East during the 1960s, would be extremely embarrassing to several nations if they were made public. All of the crew save one are willing to keep their mouths shut. That last one made the mistake of openly announcing his intention to sell the story to Time magazine before passing out drunk. By the time he sobered up, he was on a Swift Boat in Vietnam.
In Dan Abnett's Gaunt's Ghosts novel Honour Guard, Lugo's glory-seeking actions nearly lost the planet Haiga to Chaos, and as a consequence, he was dumped there as Imperial Governor. Then, that meant, in Sabbat Martyr, he was there for the return of Saint Sabbat. That, however, does not go all his way.
In William King's Warhammer 40,000Space Wolf novel Wolfblade, Ragnar is sent to Terra as a Wolfblade, a bodyguard to the House of Belisarius, chiefly to protect him from other Space Wolves who think he deserves death, but the Wolfblades he meets there admit that most of them were sent because they weren't wanted elsewhere.
It's not completely punishment, however. Logan Grimnar, the Great Wolf, points out to Ragnar before his departure to Terra that a number of the chapter's greatest leaders have come from the Wolfblades. Those who know their 40k canon will know that Ragnar later becomes a Wolf Lord.
Happens occasionally in the Conqueror books to Chinese diplomats who screw up. Wen Chao was assigned ambassador to the Mongols and Tartars after missing a meeting due to a night with a particularly good prostitute, and everybody at Shizuishan fort is a screw-up in some way.
In Phule's Company, Space Legion captain Willard Phule is sent by vindictive superiors to lead Omega Squad, the remote dumping ground for the Legion (which is pretty much a dumping ground itself.) Reassignment Backfire of course occurs almost immediately.
The protagonist of Jed Mercurio's Ascent is sent to a remote Soviet air base within the Arctic Circle.
In Walter Jon Williams's Dread Empire's Fall, Lady Caroline Sula ends up, after more or less single-handedly defeating the rebels in the Imperial Capital and playing a major part in winning the final space battle, appointed as the Captain of a ring station...on Earth. This is considered a terrible punishment, as Earth is an insignificant backwater far from the interesting parts of the empire. Of course, Sula is a lover of Earth culture and history and couldn't be more pleased.
In Diana Wynne Jones's novel Hexwood, the Bannus was placed in an obscure base on the backward planet Earth, once a convict colony, to keep it out of the way. A crooked computer clerk was then assigned to that obscure base after joining the secret organization that rules the galaxy, because he wasn't quite trusted. Which allowed him to wake the Bannus up and set everything off. He isn't a main character at all, by the way.
In the first Honor Harrington book, the title character is stationed at Basilisk Station due to being handed a Flawed Prototype of a weapon system crammed into a ship too small to make good use of it and being made to carry the can because it failed to perform well in trials, which made some powerful people in Weapons Development look bad. Every officer sent to that posting before her, undoubtedly, meets this trope. She turns it into a Reassignment Backfire by actually trying—and succeeding—to accomplish the Navy's stated mission there. She even went above and beyond that, when she put down a native rebellion, as well as the Havenite covert op behind it.
In that same book was the first appearance of recurring antagonist Pavel Young, an old "acquaintance" who preceded Honor at Basilisk, and her would-be senior officer... had he not decided to leave her alone at Basilisk thanks to feeling sudden need to take his ship home for a refit. He manages to avoid being relieved of command for dereliction of duty because his father has too much political cloutnote to the point where it takes a charge of desertion in the face of the enemy, normally punishable by death, to get him merely dishonourably discharged later on, but the Admiralty does manage to get him assigned to escort duty as far away from any possible enemy action as humanly possible so he can't do any harm.
This trope is the reason for the GNS Francis S. Mueller in the Harrington short story A Ship Named Francis. It's crewed with people the Grayson Navy had promoted above their level of competence, but who haven't screwed up sufficiently to justify more competent officers taking the time and paperwork necessary to have them court-martialed and then reduced in rank or dismissed. The crew refer to the ship among themselves as "Siberia".
Lt. Matthew Askew comes to suspect that the Manties may be a great deal tougher than the 'neobarbarians' the Solarian Navy is used to beating up on. For which he's accused of defeatism, relieved from his position as tactical officer, and transferred to public affairs — on another ship. The last means that he's the only member of his first ship's company to survive the engagement with the Manties.
World War Z. The pharmaceutical executive who marketed a fake vaccine for the zombie virus does this to himself, partly because it's too cold for the virus to thrive, but also because no human seeking vengeance can hike out there to kill him.
At the end of the novel, it's stated that this is only going to delay things; the U.S. is already negotiating with Russia to make sure the lease on his Antarctic hideaway isn't renewed.
In The Magicians, it's revealed that, following a disastrous affair with one of his students, Professor Mayakovsky was reassigned to Brakebill's Antarctic campus, which is deserted except for the occasional round of fourth-year students sent to learn from him.
The Reynard Cycle: Reynard is named the Baron of Maleperduys at the end of the first book, an underpopulated fief that's mostly a forest with dangerous Chimera living in it. It's also basically behind enemy lines. The gesture was meant as an very unsubtle insult by Nobel, and no one actually expects him to go there, let alone rule. He does, leading to a fairly spectacular Reassignment Backfire in the next book.
The Night's Watch in A Song of Ice and Fire, who guard the great Wall in the frozen north, has become this. While it was once considered an honorable calling by all, it's now a joke to most of the southern realms because the Sealed Evils In A Can behind the Wall haven't been active for thousands of years. Now, only those in the North consider the Night's Watch to be a noble calling, where second sons and highborn bastards from select Northern noble houses are known to join for the sake of honor and duty, but even many in the North don't believe the ancient threat has come back. Meanwhile, most other realms in Westeros believe the Watch is guarding the world from an imaginary threat. As a result, due to diminishing supplies and lack of support from southern realms, it is also a place to send criminals, disgraced ex-soldiers and unwanted members of noble houses. Of course, after a few thousand pages, numerous epic moments of Reassignment Backfire ensue.
The Night Watch in Ankh-Morpork is likewise a repository for the dim, awkward, cowardly or suicidally outspoken recruits who wouldn't look impressive in the Day Watch, though most are assigned there in the first place rather than reassigned. Nonetheless, the backfire duly happens when their formerly-incompetent captain proves himself and is made Commander of a new combined Watch. There's still traffic patrol for Colon and Nobby (although everyone is well aware that "a chance to be 'self-financing' and not get shot at" is not their idea of a punishment posting).
In Friday the 13th: Church of the Divine Psychopath a bunch of government agents (all them, more or less, screw-ups) are sent to Crystal Lake to hunt down and kill Jason Voorhees, though a few members of the team realize this is probably nothing but a Snipe Hunt and good publicity stunt. But, this being a Friday the 13th story, things inevitably get worse.
In The Hork-Bajir Chronicles, Seerow, who gave Andalite technology to Yeerks, is sent to the Hork-Bajir homeworld because it's out of the way, and the Hork-Bajir don't have the intelligence necessary to use Andalite technology should Seerow screw up again. Of course, the Andalites didn't count on Hork-Bajir being perfect shock troops for the Yeerks...
In The First Circle State Security Minister Abakumov threatens to reassign his subordinate to Oymyakon, "the Pole of Cold, where even bears freeze".
In the Star Trek novel series Invasion, the alien Furies create a wormhole at "Furies' Point" to invade through, then vanish for about a century so that the authors can skip ahead from Original Series to Next Generation. By the time they return, the station at Furies' Point is a place for this.
In the Morgan Kane series by Louis Masterson, when the Wild West has been tamed and there's no more need for an old-fashioned gunslinger, the titular US Marshal is reassigned to Alaska. His superiors make it abundantly clear that they intend to bury him there to get rid of him, as he is described as a "walking anachronism".
The House of Life in The Kane Chronicles series by Rick Riordan has 360 nomes (That is, places that members can be assigned to). The first is Egypt, where it was founded. 360 is literally Antarctica, populated only by "a few cold magicians and some magic penguins." It is used as a punishment assignment. North Korea is also used for this purpose.
In Pantheocide, the second book of The Salvation War, this is believed to be the case for US Army personnel who run transit and orientation for living citizens visiting Hell.
In Pyramid Power, this is referred to as being 'buried alive at Thule Airforce Base'. It was probably done to a few PSA agents who exceeded their authority and offended a lot of people in power. The alternative was being eaten by an angry Sphinx.
Rally Round the Flag, Boys! begins with Guido di Maggio facing reassignment to Alaska, which he manages to avoid at the last moment by offering to conduct a public relations campaign for a Nike missile installation in Putnam's Landing, where he was born and raised and his fiancée is currently living. The civilian-hating Captain Walker Hoxie, however, is revolted at his being assigned to take command of said installation. The public relations campaign ends in disaster, and Guido ends up sent to Alaska anyway.
This is how the plot of the The Robe by Lloyd C. Douglas is kickstarted when this trope happens to the protagonist Marcellus.
The Thieves' World anthologies begin with this. The Emperor has a young, charismatic, and, unfortunately, naive half-brother; he's a constant magnet for plots and conspirators, but the Emperor isn't willing to have him killed when he hasn't done anything. Solution: assign him as governor of the small, recently conquered, barely pacified, out-of-the-way border town of Sanctuary...
John Hemry's Stark's War trilogy involves U.S. soldiers stationed on the Moon. At one point, Stark, having taken command, warns that if one of his subordinates takes her wheeling-and-dealing ways too far, "I'll post her on sentry duty at the lunar pole for so long she'll think she's a space penguin."
In Rick Cook's Limbo System, about a third of the people onboard were sent as punishment or exile of some kind.
In Tom Sharpe's Wilt on High, the hapless security officer at the USAF base in Cambridgeshire (which Henry Wilt manages to reduce to inoperable paralysis) is eventually re-assigned from his plum posting in England to duty in Nome, Alaska.
America (The Book) mentions that Ambassadorial duties tend to take the form of a) old friends or campaign backers of the President being assigned to nice places, and b) people who annoy the President being banished to some mosquito-infested backwater nobody cares about for a few years.
In the Agent Pendergast novel Book of the Dead, Agent Coffey threatens the guards with demotion and transfer to North Dakota. When everything comes crashing down on him, Coffey is heavily demoted and transferred to North Dakota.
Vanity Fair: The Marquis of Steyne arranges to have Captain Crawley made governor of remote Coventry Island after Crawley catches his wife Becky in a compromising position with the Marquis.
In the novella Le Silence de la mer, set in Occupied France, Werner becomes utterly disillusioned with the conduct of the war and requests a reassignment to the Eastern Front.
Inverted in Ciaphas Cain: the titular character wants nothing more than a backwater assignment wher he won't get shot at, and does his best to arrange it via gambling, blackmail and charm. Unfortunately, even when he does manage to do so, it only serves to uncover the local genestealer cult/Chaos plot/Necron tomb, resulting in half a dozen life-threatening situations, another medal or two and the brass sending him out to the frontlines again. Or so he says, as it's implied several times he gets bored rather easily.
In Servant of the Empire, after Tasaio's elaborate multi-year effort to kill Mara fails, he is assigned to anti-piracy duties at a fortress in the Outpost Isles. The last pirate activity in the area took place a century and a half earlier.
Bateman, the bartender, in Clocks that Don't Tick once attempted to escape his servitude to the Bosses. In response, they forced him to work alone at a bar. What especially sucks about it is that nobody in the area has money for drinks. Charlie was apparently his first customer (and the first person) he has seen in years.
Happens quite literally in The Supernaturalist when Ellen Faustino survives. Her boss admits that the Un-spec Four project was going well before the Supernaturalists came and exposed it, and since everyone thinks she's dead, she's allowed to continue it. But since they need to be "sneakier" about it, she has to continue it in The South Pole.
In Paranoia, Adam Cassidy reads up on Golddust, an old and obsolete technology compared to wifi. He tells Nora, his manager, about a rumor he heard about how it is obsolete and how Sony isn't going to go with it. Later, he gets a good plan of action on how to use Golddust for military purposes. The head of the company, Goddard, approves of this plan. Nora, wanting to get rid of someone who showed her up in a board meeting in front of her boss, puts in to transfer to North Carolina. He is saved at the last minute by Goddard making him his personal assistant, as he was rather impressed by his notes in the meeting.
While not a literal example, in the Judy Moody books, students in Judy Moody's class who act up or act out get sent to "Antarctica," which is a desk in the back of the classroom and nobody wants to be sent to Antarctica. Judy, being as moody as her name, spends a fair amount of time there.
At the end of the Relativity story "Target", General Lira gives his son, Oscar the position of Ambassador to Spain just to get him as far away as possible.
Joe Pickett: When Joe is reinstated as a game warden after being fired, he is assigned to the remotest of Wyoming's game districts: a place with a reputation of a place where wardens are sent to either be forced to resign, or wait out the rest of their careers till they die.
The Dolphin Ring: In The Silver Branch, Justin and Flavius are Kicked Upstairs to Hadrian's Wall after accusing Allectus of conspiracy. They realise later that Carausius put them out of Allectus's reach.
In the Able Team series, a CIA spymaster sends his minions to attack Carl Lyons. They do so despite Carl being a known badass, as Carl could send them to hospital, but their boss could send them to Nicaragua.
The ultimate fate of Captain Neals in Alexis Carew: Mutineer. For losing his ship to a mutiny he created through his own brutality, and for disrating Alexis when she refused to Kneel Before Zod, he's suspended for psychiatric reasons with a promise that if he ever returns to active duty, he'll be stuck safely ashore under an admiral's direct supervision, and possibly promoted to Admiral of the Yellow (junkyard detail).