Applied Phlebotinum with one specific quirk: you cannot get rid of it. It cannot be removed, lost, given away, buried, thrown in the ocean, blown up, or separated from the owner in any way. It's usually not intelligent or sentient, but is nonetheless bound to you, for better or worse, till death do you part.
This can be found in Fairy Tales, particularly those where Self-Fulfilling Prophecies are not to be thwarted by a condition such as "You have to get this ring back to marry my daughter."
The most benign form is an Empathic Weapon that's a little too empathic. It's not necessarily something you would want to get rid of, but it can sure make maintaining the Masquerade much harder if your Glowy Sword of Doom simply will not let you leave it at home. Also, if a villain is after it, you can't easily comply with a demand to hand it over to save a friend. In this case, the only chance they have of getting it is killing you.
The evil version is more like an implacable stalker. From the moment it crosses your path, no matter what you do to get rid of it, it will always be there. If you're lucky, it will just make you a Weirdness Magnet. If you're unlucky, it'll be an Artifact of Doom that will make your life a living hell until you fulfill The Quest to destroy it or seal it away for the next hapless victim.
If a Clingy MacGuffin appears in an ongoing series, expect several episodes about the character's attempts to get rid of it so that he can lead a normal life. He might even succeed a couple of times but circumstances will always manage to bring the two of them back together because otherwise, there wouldn't be a show. The character might also come to accept or even enjoy their new life and actively seek to regain the Clingy MacGuffin.
If the MacGuffin is a piece of clothing, it's a Clingy Costume. If it's a living thing, it falls into The Cat Came Back. Compare Loyal Phlebotinum, which can be physically separated from the owner but still only works for its Chosen One.
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Technically, any comedy in which a hapless person gets something — a paintbrush, a Post-It note, etc — physically glued to their body and can't dislodge it could qualify as a (non-magical) descendent of this trope. If the attached object is relevant to the plot (e.g. the accidental lipstick stain that can't be wiped off, sabotaging the protagonist's romantic chances with his girlfriend), it actually is this trope.
This is a major theme of Yu-Gi-Oh! ZEXAL. All of the Numbers (except for Number 39: Utopia, maybe) are malevolent beings that corrupt whoever owns them, each causing its host to become drunk with power and become obsessed with it. What's more, the Numbers Holder is driven to find other Numbers by it. There are people, whoever, who are immune to this effect and those who can resist it, mostly Numbers Hunters like Yuma and Kaito, but they usually have some supernatural or technological aid.
The title character of Gokudo planned to abuse his magic sword in a similar manner as in Dead Last, though his genie stops him before he can even try.
The G Units from Guyver cannot be properly removed from their hosts without a specific piece of technology. Tearing out the control metal causes the armor to actually consume its host, but the metal regenerates the host shortly after.
The Blue Water from Nadia: The Secret of Blue Water. There's a moment when she throws it into the ocean, only to have it rise from the waves and return to her.
When Ichika from Uta Kata tries to throw away the charm given to her by Sei, it just flies back to her, signifying that it is too late already to change her fate.
Mahoujin Guru Guru has an award statue that reappears whenever Nike tries to dispose of it.
The ginzuishou from Sailor Moon qualifies. Despite the canon belief it can be taken and in the anime it is passed on, present Usagi always, always, has a copy of it. Even when Chibi-Usa takes the future version, Usagi still has the past version. Usagi eventually gets that copy back as well. In the manga, Chibi-Usa even gets a new pink crystal so Usagi can keep the ginzuishou.
A "kinda" example from Legendz: in the first episode, Shuu tries to get rid of his Talispod, but the wind blows it back to him.
In a Slayers OVA, Naga, on pure impulse, put on a valuable bracelet made out of rare Orichalcum. Unfortunately, she discovered that she could not take it off. And what's more, a powerful superweapon became attracted to the bracelet and Naga and Lina got chased all over by this creature.
Kazuki's kakugane in Busou Renkin, which had been put in his heart's place by Tokiko so he could survive a mortal attack from a homunculus which she was trying to kill. From this, the whole story kicks off, and halfway into it we find out that the kakugane is of the black variety, which tends to make the user absurdly powered, but he has to nourish on other people's energy to subsist.
The title item of Witchblade is a strange bracelet that turns the user into a Stripperific death machine. Its clingyness is demonstrated in a sad sequence when Masane tries to get it off... using dangerous tools that could cost her an arm. At one point it wakes up, slices a press into ribbons and goes back to sleep. Worse, if Masane dies, it passes on to her daughter. Eventually she sacrifices herself, taking the Witchblade with her.
Ichigo's Hollow mask in Bleach. If removed from his person it will disintegrate into nothing, but it always reappears on him, appearing to block fatal blows early on. When his Hollow gains enough power to start interfering in Ichigo's fights, it becomes downright dangerous. The "Hollow" is revealed much later to be his true Zanpakutou spirit Zangetsu; the "Old Man" really being a manifestation of his Quincy heritage. Ichigo can't get rid of it because it's part of his own soul.
InuYasha: Kaijinbou forges Toukijin but cannot get rid of it. It controls his will, driving him to hunt Inu-Yasha and eventually (accidentally) killing Kaijinbou through sheer force of power. Death doesn't separate them, Toukjin just animates Kaijinbou's body and keeps going. In the end, Inu-Yasha has to hack off the smith's wrist to separate them, which allows the dead body to disintegrate, leaving Toukijin behind. When Sesshoumaru touches Toukijin, his will is so powerful it instantly defeats Toukijin's power, turning Toukijin into a Loyal Phlebotinum instead.
A chapter of the Ranma ½ manga has female!Ranma ending up in a cursed swimsuit with the talking figure of a devil dog adorning it. No amount of efforts can remove it (panda!Genma gets near it with a pair of scissors, but the devil dog's face eats them). The only way to get rid of this curse is to fulfill the swimsuit spirit's wish before the sunset... or it will drag Ranma to the bottom of the sea.
In the card game Munchkin, there is a curse called "cursed thingie". It curses an equipped Item, which then doesn't give any bonuses anymore and can't be removed voluntarily. The result is, that it still occupies its slot (for example footgear), therefore blocking it. Therefore, the cursed player wants it on an item which is small and does not occupy a slot or hand. The other players want it on something that occupies both hands or a slot and is big, for maximized inconvenience.
Pierino e il burattino (Peter and the Puppet, an Italian comic, by Antonio Rubino, 1919) used this trope as subject. Obsessively. Although defining the puppet as Applied Phlebotinum can be excessive: it has no apparent property or power, but it comes always back to its unwilling beholder.
One of these features prominently in one of the issues of the Spanish comic Mortadelo y Filemón, titled "The Warlock": a magical note, enchanted to kill anyone who reads it. The titular characters subsequently try to remove it by the most varied means, chucking it into the bin, triturating it, burying it, tying it to a rock and throwing it to the sea, and hitting it with a full discharge of a flamethrower. And yet the note manages to never be actually harmed due to some kind of karmic immunity that causes people around it to suffer instead.
A villainous example occurs in the Iron Man comics with the Mandarin and his alien rings, which give him a variety of fantastic powers. The rings are attuned to him and cannot be taken from him by force. A partial subversion comes from the fact that the Mandarin can voluntarily lend his rings to his minions, although if they're knocked out or killed the ring automatically comes back to him. If the Mandarin himself loses consciousness, all the rings automatically reappear on his fingers, which left his Mooks powerless to stop the Stark employees they had kidnapped from escaping on one occasion after Iron Man knocked out their boss.
Shows up in Green Lantern on occasion. When Hal Jordan was given a Blue Lantern ring, he was unable to remove it without hoping for something. In a Green Lantern cameo on Superman: The Animated Series, Kyle Rayner couldn't remove his lantern ring even when he tried.
Spider-Man. The alien symbiote-suit that does get forcefully removed (although not easily), and promptly sees about finding itself a more appreciative host (thereby becoming Venom and its offspring, Carnage and Toxin). Even having successfully removed this MacGuffin from his body, the Web-slinger still isn't free of it: year after year, host after host, it comes back to fight him. It also has a "crazy ex girlfriend" thing going on, and several comics have stated that it would gladly go back to Peter if he accepted it, which means it's still trying to be even clingier.
Conan the Barbarian once came into possession of the Ring of Molub, an artifact connected to an ancient, Nigh Invulnerable demon of the same name. The demon will relentlessly pursue and slaughter the bearer of ring, which can only be disposed of by passing it on to someone without their knowledge, condemning that poor bastard to an extremely horrific death. Conan gets rid of it by slipping it on the finger of that story's Big Bad … and then breaking his hand for good measure.
The Pistols in The Sixth Gun bond to whoever picks them up after their previous owner dies. Anyone else gets burned by green fire.
Parodied in Tintin, with the piece of sticking plaster from Tintin The Calculus Affair. When Captain Haddock tosses it off, it sticks to someone else, who in turn shakes it off. And so it goes all over the bus, before coming to the Captain's cap. It then follows him aboard the plane, eventually makes its way to the cockpit (causing the pilots to momentarily lose control), lands on the Captain again by the end of the flight, is thrown away at the police station, only to return yet again on the captain's clothes in the hotel room!
The Blue Beetle Scarab is "permanently" infused on the back of adorkable Jaime Rayes that turns him into the 3rd (rightly named) Blue Beetle.
In a story called "The Sliceman Cometh", in issue #44 of Tales from the Crypt, a French Revolutionary executioner who'd killed an innocent man at the request (and payment) of the victim's brother kept trying to dispose of the head only to have it returned to him in various plausible ways. Finally he decided to chop it to bits — which was when the headless corpse showed up looking for it...
The Star Brand of The New Universe, an energy source that can do anything the user wants to. However, even if you do find a way to get rid of it, a piece of it will still live on in you and recharge itself.
The current Crimson Avenger is a woman who bought a pair of Colt handguns to exact revenge on a murderer who escaped justice. The guns are cursed, and bonded permanently to her hands. They also lack triggers and never need to be reloaded, apparently firing by themselves and using her as a "host", to bring about vengeance on those who go unpunished for their crimes. She gets an "assignment" by reliving the death of the killer's victim, then involuntarily teleports to the killer's location. One time she tried to kill herself instead, but the guns render her immortal.
The quantum bands that come with the job of Protector of the (Marvel) Universe, once put on, don't come off again until the death of their wearer. As a result, Quasar gets killed once precisely because the Big Bad of that story arc is after the bands and discovers that the bands can't even be removed from his wrists after cutting off his lower arms. (He does eventually get better.)
There's a Mickey Mouse comic that combines this trope with Mundane Utility. Mickey receives a cursed miniature sculpture that is so ugly that no-one wants to keep it, but it will remain with the person who found it until they can find someone else to voluntarily accept it. At the end he is still unable to get rid of it, and finds a cave filled with thousands of identical copies of the object. After thinking for a bit, he makes them into keychain holders and starts a booming business selling them, as whoever buys one will never lose their keys again.
Loki's Mask from The Mask (the Jim Carrey movie) falls into this category: when Stanley tries to throw it out the window, it boomerangs right back to where he picked it up from. It also functions in a Hostage for MacGuffin scenario, although this is subverted by the fact that Stanley himself is the hostage, trying to save his own life.
In Click, the "Universal Remote Control" given to the main character. In one sequence, the character tries to rid himself of the device, but it returns in a variety of hilarious ways.
Michael Newman: Oh, yeah? I'll take my clothes off. Then what's—? Morty: I wouldn't do that if I were you. There's only one place left for it to pop up.
In Help!, this is taken to the point of absurdity: Beatle Ringo Starr has an Eastern sacrificial ring stuck on his finger, and nothing anyone can do (and everyone tries) can get it off. It can only be removed by an act of courage from Ringo, so it isn't until the end of the movie that it gets removed.
In The Gods Must Be Crazy, Xi's tribe tries to throw the Coke Bottle away, but it keeps coming back (occasionally causing mayhem in the process), leading up to Xi's Quest to throw it off the edge of the world.
Once the ruby slippers in The Wizard of Oz appear on Dorothy's feet, they become stuck and won't come off, something the Wicked Witch of the West remembers the hard way when they shock her as she tries to remove them.
In The Mummy Returns, Alex tries on a bracelet that turns out to be the key the bad guys are looking for. It's not detachable.
In Oscar, there is a subplot revolving around three identical valises — one containing money, one containing jewels, and one containing the maid's clothing and undergarments. The police and other gangsters are made suspicious by the way the valises keep going in and out of the house, but whenever a valise is seized and opened, it is invariably the one that contains the maid's clothing. This leads to a Crowning Moment of Funny late in the film.
Indiana Jones's fedora. Through all four movies (and the video games, as well) it's constantly with him, and seems to follow him everywhere when he's not wearing it. See toward the end of Last Crusade, where Indy sits resting after the tank fight and the wind magically blows his hat back to him.
The bracelet-gun in Cowboys and Aliens. Later subverted when it turns out he just didn't know he needed to empty his mind of thoughts in order to unlock it.
Pipe Down, a title in the Super Mario Bros.Nintendo Adventure Books gamebook series, has this happen to Princess Peach when she receives a mysterious pair of red sneakers for her birthday. When she puts them on, they begin forcing her to dance a la the Hans Christian Andersen tale, and she eventually becomes the unwilling star of a Koopa basketball ballet. If Mario and Luigi manage to find her in the desert in one sequence, she'll tell them that she's tried over and over again, but the sneakers just won't come off her feet.
The hero of J.H. Brennan's Saga of the Demonspawn gamebooks, Fire*Wolf, comes across a sentient magical sword that he keeps with him because it's a powerful weapon. It's only later that he learns he was destined to inherit it and finds he can't get rid of it. At the end of the series, when the Big Bads try to cripple the hero by stealing all his weapons, they find they can't deprive the hero of the sword.
In The Fabled Lands if you earn the favor of Nagil, the god of death, you can be gifted with his White Sword. Besides its staggering +8 combat bonus, you'll have it forever. Even if you die and are brought back to life, you'll lose all the rest of your stuff, but not the sword.
In the Undead... Series by Mary Janice Davidson, there is the Book of the Dead.
The young adult novel The Eyes of Kid Midas features a pair of sunglasses that allow the wearer to change reality any way he wants... but the glasses cannot be removed.
The short story "The Zahir" by Jorge Luis Borges involves a variant on this trope. The title object is cursed, causing anyone who sees it to become gradually unable to think of anything else. The main character succeeds in getting rid of the zahir itself, but is unable to get it out of his head.
Another Borges example is "Shakespeare's Memory". The narrator — a German Shakespeare scholar — meets a man at a party and unwittingly agrees to accept Exactly What It Says on the Tin: the personal knowledge of all the experiences of William Shakespeare, recollections of which encroach more and more upon his thoughts, threatening to displace his own identity. He can only get rid of it by convincing another person to willingly accept it.
The John Bellairs novel The Spell of the Sorcerer's Skull features a miniature skull that can fit in a pants pocket... and returns there after the protagonist drops it into a lake.
The walking stick in Iron Kissed, by Patricia Briggs. The protagonist Mercy Thompson acquires a magical walking stick, exact properties unknown. She tries to return it to the fairies several times, but it keeps coming back. A slight twist in that the stick shows up "in places where I live", like in her bed, her car and her work area. Mercy later uses this fact to lure her attacker into a trap. She could have retrieved the stick from any area she spent time in, but only told him about the spot that was protected. Apparently, it also has the power to ensure that all the owner's ewes will bear twins — not particularly useful for a Volkswagen mechanic. It comes in handy in Bone Crossed — apparently it was made by Lugh of the Shining Spear, and so can be used as a spear when needed.
Vain from Stephen Donaldson's second Chronicles Of Thomas Covenant trilogy, who was brought to life to serve some mysterious purpose. He doesn't actually do much except hang around grinning like an idiot, but he's virtually indestructible and has a knack for overcoming insurmountable obstacles to return to the protagonists whenever something detains him. Not so much a case of The Cat Came Back because, as it turns out, he's an embodiment of pure order that will become one-half of the new Staff of Law when combined with an embodiment of pure magic.
In Robert Louis Stevenson's story The Bottle Imp, the title MacGuffin (Exactly What It Says on the Tin, it's a bottle, with a devil inside) grants the owner's wishes... but the only way to get rid of it is to sell it at a loss, and still having it in your possession when you die means eternal damnation. The problem is averted when the bottle ends up sold to a minor character who doesn't care about the cost because he fully expects to go to hell anyway, and exchange rates permit the sale even when the bottle was bought for a single penny.
The Power of Stormhold in Stardust, which Yvaine must carry until the heir of Stormhold asks her for it. But we don't know how clingy it is, because she never actually tries to get rid of it in any other way. In the book, Yvaine's lugging the gem around is explained as an obligation — though it knocked her out of the sky it's not hers, and as stars take obligations very seriously, she can't just leave it. She dislikes having to carry it, but will not get rid of it until the right person asks — that would be inexcusable for any star. A sort of culturally-induced Clingy McGuffin.
Elric, Last Prince of Melibone, is a sickly albino who keeps himself competent as a Badass cliché hero through drugs, magic, and his evil Empathic Weapon, Stormbringer. After destroying his kingdom and losing his true love he has a narmy sequence where he tries to get rid of it and it stands in the ocean smirking at him and Elric becomes... very dramatic on the topic of realizing he's stuck with it. Bonus points for the illustration: it is in the fantasy-illustration style that includes every tiny detail of his outfit, and he gives an impression of faking female orgasm. Of distress. Possibly fainting, too. Perfectly normal for his type, really.
A dragon scale keeps appearing in the path of the heroes in Mercedes Lackey's One Good Knight in her Tales of the Five Hundred Kingdoms series. Fortunately, the Genre Savvy Sir George knows better than to disturb it; they eventually find that a fox has been following them and moving it around. In fact, the Tradition is a reliable source of Clingy Macguffins — if it's Traditional for a wizard to have a stuffed alligator in his office, he will have one there no matter how often he disposes of the existing one. The only way to escape Tradition is to shift one's personal circumstances so that they no longer suit that particular tale.
Need from the Heralds of Valdemar books takes the direct approach. Unless Need wants to change bearers, trying to get rid of it takes a fair bit of willpower, causes all manner of Nightmare Dreams, and frankly hurts. Just trying not to use it takes an act of will. However, once Need becomes fully conscious, she is no longer clingy.
Tarma and Kethry, in one of their short stories in Oathblood (of the Heralds of Valdemar series), find a cursed bad-luck coin in their possession. They can't get rid of it in any ordinary fashion, but they do manage to find a way to pass it onto a more deserving group. It required considerable self-sacrifice on their part, with someone else inadvertently taking it.
The Luggage and Rincewind in many of the books, which can follow its owner to nonmagical worlds and the end of time itself. The Luggage is made of sapient pearwood, a rare wood that grows in high-magic areas. Anything made of sapient pearwood gains virtual immunity to magic and the ability to follow its owner anywhere in the multiverse, which is why a traveling chest made of sapient pearwood is said to be more valuable than anything and everything that said chest could possibly contain. And given that it's also a Bag of Holding, that can be quite a lot of stuff.
In Wintersmith Tiffany's horse pendant turns out to work exactly as the ring in the folk tale; she gets rid of it near the start of the book to keep the Wintersmith from finding her, and near the end of the book finds it in the guts of a pike caught by her little brother.
Slappy the recurring Demonic Dummy and his one-shot equally evil peer, Mr. Wood.
Inverted in another book, with a demonic sponge that kills the possessor in 24 hours if left alone. It made a habit of running off to try and kill the protagonist.
The Haunted Mask, which is incredibly difficult to remove once you put it on. In fact, it claimed the faces of several previous wearers.
In The Green Pearl by Jack Vance, the eponymous green pearl is so beautiful that it fills the hearts of everyone who sees it with greed. Unfortunately, the pearl is cursed: no-one will buy it, and if thrown away or given away it will always return to the current owner (even if it has to animate a corpse to carry it back). It can however be transferred by being stolen, which half the time involves the murder of the current owner.
The Misenchanted Sword by Lawrence Watt-Evans is about a sword that is a flawed Clingy MacGuffin. It makes one almost invincible in single combat (against adult males) about 100 times — then will pick a new owner and kill its old owner. And each owner will get betrayed faster. When sheathed the sword must stay within a certain distance from the wielder, but it becomes far more clingy once drawn and prior to killing; the blade must maintain contact with the wielder at all times. Trying to throw it away or hide it won't work, and is dangerous — the spells used cause an earthquake to return it at one point. On the other hand, nothing except the sword can kill its owner. The way the owner deals with it is refreshingly different than you'd expect: he used it as a mantle piece. Someone tried to steal it, and the resulting chaos almost wrecked his bar. Finally he got tired of it and just kicked it under his bed.
The title painting in Stephen King's short story The Road Virus Heads North, which not only shows scenes of mayhem occurring in its wake, suggests that the subject of the painting is following the protagonist and fully intends to kill him as well when he catches up. It is suggested that the painting cannot be gotten rid of or destroyed by any means. It's also suggested at the end that the painting isn't actually a painting, but part of its painter's ghost; the other part is hunting after the protagonist.
The creepy monkey in King's short story "The Monkey" is also resilient and extremely hard to get rid of.
The One Ring from The Lord of the Rings could perhaps be considered one of these: there's a moment, for example, in the first chapter of The Fellowship of the Ring, when, as Bilbo is preparing to leave the Shire, Gandalf persuades him to "stop possessing it, give it to Frodo", and Bilbo agrees, but as he walks out, Gandalf stops him: "You have still got the ring in your pocket." The Ring also attempts to compel its wearer to put it on when a Ringwraith gets near. However, it could also be seen as a partial subversion of this trope, as it also has a tendency to slip off the bearer's finger unexpectedly, often when it is most needed; this is how it came to Bilbo after slipping off Gollum's finger. It also slipped off of Isildur's finger, revealing him to a band of orcs, thereby betraying him to his death.
In the book it is noted that even if thrown into the sea it would eventually find its way back to civilization by compelling some fish to eat it, and if buried under a mountain it would gnaw on the minds of the person who knew its whereabouts. (And imagine having the willpower to throw even an ordinarily priceless item such as the diamond in Titanic into the sea.) Anyone sufficiently powerful to safeguard it would be tempted to claim it and become the new Ring lord, and it would try to slip away from anyone sufficiently weak to avoid temptation or ability to wield it — and slip into the hands of someone who could.
The film explained this fairly concisely. The ring cannot be destroyed, except for within Mount Doom. The Ring cannot be guarded, buried or lost again; it will always call out to the nearest person to possess it, and cannot be resisted for long. The Fellowship could not be avoided.
Another Tolkien example, from The Silmarillion, is the Silmarils and the Necklace of the Dwarves (which was built around one of the Silmarils). Morgoth is unable to part with the Silmarils even though their holy light burns him, and later Beren is unable to throw away the Necklace when he is told to, instead giving it to Lúthien to wear.
Played with in Gene Wolfe's Book of the New Sun series, which takes place billions of years in the future. The hero, Severian, believes that the tiny claw shaped piece of Lost Technology called the Claw of the Conciliator that he had been carrying with him for a while was destroyed in an artillery bombardment. However, he later pricks himself on a bush and finds that the thorn is the Claw. However, later he discovers that he had actually subconsciously created a new Claw using a psychic link to some Imported Alien Phlebotinum that he did not know he had. He later goes back in time and gives the new Claw to the same religious order that he got the old one from, creating a Time Paradox. During the same time trip he acquires his link to Imported Alien Phlebotinum from Sufficiently Advanced Aliens, giving his younger self the power to create the Claw.
In Harry Potter and the Deathly Hallows, it is implied that the Elder Wand can't simply be destroyed: neither McGonagall nor Harry think about it when the chance presents itself. Though Harry does believe Dumbledore's plan will work — if all goes well, at least. The Elder Wand can be passed on fairly easily, the wielder just needs to lose a fight. The curse, so to speak, comes from the fact that it was usually passed on by lethal force.
In Wicked, when Elphaba finally confronts Dorothy, she demands Nessarose's silver slippers, which Dorothy is wearing. Unfortunately, Dorothy finds that the slippers won't come off her feet, much to her and Elphaba's mutual frustration. Dorothy Lampshades this trope by stating that she's been trying to get the slippers off for days... and now her socks are so sweaty that "it's not to be believed."
Percy Jackson and the Olympians: Percy Jackson's magic pen/sword Anaklusmos ("Riptide") can't be lost. Every time it's seperated from Percy, it simply returns to his pocket as a pen.
In David Eddings' The Belgariad, Princess Ce'Nedra is given a magical amulet by Belgarath, Polgara, and Garion that once belonged to Garion's ultimate grandmother. Once accepted and donned willingly, it cannot be removed by anything short of the wearer's death. Being the Alpha Bitch as well as a Tsundere, Ce'Nedra at first bursts into tears thinking they are giving her a symbol of enslavement, but later discovers that the amulet gives her unique powers of perception.
The Device of Time Journeying in Weis and Hickman's Dragonlance novels stays with the person to whom it is given.
Robert Westall's The Cats of Seroster features a knife that conveys immortality on its owner and if you try to discard it will come back to you or bring you back to it. The only way to get rid of it is to trick someone else into taking it.
The chain letter in Chain Letter by Christopher Pike. Once the letter is sent to you and you are on the list, the only way to free yourself from eternally being commanded to perform tasks (each task progressively becoming more malicious and difficult) is death.
In John Bibee's Magic Bicycle series, most supernatural objects are like this, especially number cards.
In Larry Niven's short story "Not Long Before the End", the barbarian warrior Belhap Sattlestone Wirldess ag Miracloat roo Cononson (his friends, who tend to only be temporarily so, call him "Hap") is rightly proud of his magical sword, Glirendree, and the fact that he cannot put it down or let it go doesn't really bother him... until the Warlock informs him that Glirendree is actually a demon forced into sword-form, and the reason he cannot put it down (or even transfer it from his right hand to his left) is that the demon has already sunk its fangs into his hand.
In Robert Mc Closkey's story "Pie and Punch and You-Know-Whats", a stranger slipped the main character a record containing a ditty which, once heard, compelled the listener to keep singing parts of it over and over, "infecting" anyone who hadn't previously heard it with the same misfortune. It referred to, and was presumably inspired by, a similar story by Mark Twain called "Punch, Brothers, Punch."
E. E. “Doc” Smith's Lens is this after a fashion. Yes, those who acquire it do so deliberately and in full knowledge of the cost, and the thing is not intrinsically troublesome, but earning it elevates one to a rank that carries grave responsibilities for all its wearers; promotion to the elite ("Unattached" status) carries a 90% mortality rate (and the survivors are mostly artificial parts); and you can't ever give the thing away because it'll kill anyone who comes into more than fleeting contact with it. Come the final battle against the Eddorians, even Lensmen long since retired are required to do their bit.
In The Wizard Of 4th Street, the runestones keep reappearing in the pockets of Wyrdrune or Kira when they try to sell or discard them. Later, when they're joined by Modred, the three stones fuse themselves with the three characters, becoming permanently Clingy.
Michael McDowell's novel The Amulet features the title amulet as an Artifact of Doom that is passed from resident to resident in a sleepy Alabama town. Anyone who stumbles across it is invariably compelled to hold it up around their neck and press the ends of its broken chain together, often to imagine how it would look on them. The chain then magically fuses together, resisting any subsequent efforts to remove it - until after the wearer has perished in a terrible freak accident, after which it comes loose of its own accord for the next unsuspecting victim to find.
Rhodry's silver dagger in Katharine Kerr's Deverry series.
In one of the stories from Uncle Montague's Tales Of Terror, The Demon Bench-End, the eponymous item is this, overlapping with Driven to Madness and Driven to Villainy. Moreover, its current owner cannot get rid of it on purpose - it has to be stolen from them. It's implied that attempting to destroy it simply causes the owner to destroy something that they hold dear instead.
Louisa May Alcott wrote a considerably more lighthearted and benign version of Andersen's The Red Shoes with The Skipping Shoes. A naughty girl named Kitty puts on a pair of new shoes that force her to behave, and that won't come off her feet when she tries to remove them. The shoes do have their upside, as when Kitty starts trying to be nice the shoes actively help her do it. They also give her the ability to talk to animals and even start teaching her how to dance. While their magic wears off at the end of the story, Kitty learns that Good Feels Good and continues to act as if she was still wearing the shoes.
The Amanda Show has this played for laughs — Amanda's character (in a sketch) was trying to sleep, only for the doll to be constantly talking and wake her up. She even throws it out the window, and then it jumps back in. She has her dog eat it, only to hear the voicebox still functional.
In the short-lived series Dead Last, the Talisman owned by the main characters that allowed them to see ghosts always returned to them, no matter how they tried to dispose of or destroy it. One character actually took advantage of this in different ways - for example, he pawns it repeatedly in the first episode and makes a sizable sum of money.
Parodied in Everybody Loves Raymond with the canister episode. A jar to hold crayons and cookies becomes symbolic of Marie's never-ending hold on Debra and the Barone family.
The demonic vessel box that holds the Weapon of the Week in Reaper.
LOST's mysterious numbers are an intangible but Clingy MacGuffin for Hurley. They keep turning up, though Hurley runs from them at every turn.
A non-magical example occurs on Ally McBeal when the title character is dragged to a bowling alley by her friends after work. Since she doesn't have a ball, she borrows one from another bowler. Unfortunately, Ally's fingers swell up in the holes and the bowling ball becomes stuck to her hand. She tries to get it sawed off, but the bowler she borrowed it from pleads with her not to do it, since it was a memento of his dead wife. Ally is forced to take the ball with her to the office the next morning, just as they're about to try an important case. Fortunately, the swelling in Ally's fingers goes down and the bowling ball slides off... only to land right on her foot.
In Smallville, Clark Kent at one point is tricked into putting on a ring that takes away his powers. It wouldn't come off and was seemingly indestructible (it was unaffected by Clark using a grindstone on it). He considered cutting his finger off, but Chloe begged him not to, so he didn't try. It took the power of the Fortress of Solitude to get rid of it.
A benign example of this, similar to the Ring of Polycrates story, can be found in the miniseries The 10th Kingdom. Wolf purchases an engagement ring for Virginia, and after being rejected, he throws it into the lake. At the end of the story, Virginia ends up ordering the fish that ate the ring and Wolf takes this chance to propose again, with greater success.
The Glove of Myneghon from the Buffy the Vampire Slayer episode "Revelations". It's an all-powerful gauntlet that will not release its hold on the wearer until death.
Rodney once found an Ancient force field device that protects its wearer. Since he's... well, Rodney, his fear keeps it from ever deactivating, protecting him from bullets, falls,eating (his fear of random accidents was greater than his fear of starvation), etc. At least until he realizes it makes him the perfect candidate for a dangerous mission, at which point it promptly falls off.
In the episode "Tracker", the Runner Kyrik (Runners are human big game prey for the Wraith) is in possession of an ancient armband artifact that fused onto him, and allows him to teleport long distances as long as it's powered up.
In Chuck, the title character accidentally has a database of government information uploaded into his brain, setting off the events of the series. A recurring storyline is Chuck's attempts to have the Intersect removed. Though he succeeds a couple of times, circumstances usually force him to re-upload it.
In The Invisible Man, an artificial gland that allows a person to become invisible is implanted into a convict named Darrien Fawkes. The only person who can remove it is killed by the series Big Bad, who wants control of the gland.
The baseball from Defying Gravity in the episode "Rubicon" is a variant on this. It is a symbol of Donner's unresolved guilt for being forced to leave his girlfriend to die on the Mars mission. Once in each of the two time periods that the episode takes place in Donner gives the baseball up; both times he gets the ball back. The episode ends with Donner chucking the ball out the airlock, a symbol that he's finally given his guilt up.
The story of the ring that returns to the owner (and often carries with it a bad omen) is Older Than Feudalism. It goes back to Ancient Greece, but appears in folklore in many variations: The oldest version is probably the story of Polykrates, tyrant of Samos, as recounted in The Histories by Herodotus of Halicarnassus (5th century BCE). Polykrates threw a precious ring into the sea as sacrifice to the gods, because his friend, the pharaoh Amasis, was afraid that Polykrates' legendary luck might anger the gods and they would destroy him. A few days later, a fisherman caught a beautiful fish and brought it to his king as a gift. When the fish was cooked and cut open, Polykrates' ring was found in its belly. A bad omen, since this meant that the gods had rejected the sacrifice. The German poet Friedrich Schiller based his poem "The Ring of Polykrates" on Herodotus.
In Schiller's poem, the Genre Savvy friend immediately packs his bags and leaves, because somebody with that good luck is bound to get Karma Backlash soon.
The English fairy tale "The Fish and the Ring"  is named for its use of this trope: the baron is trying to forestall a Self-Fulfilling Prophecy by refusing to let his son live with his wife, a peasant girl, until she presents him with a ring he threw into the sea. She takes a job as a cook. He is served a dish containing fish — and the ring. The girl had cooked it. He ceases to resist fate.
Also happens in a tale told about Saint Mungo — in this case, the ring clears a queen of infidelity. The fish and ring are on the Glasgow city coat of arms.
The Brothers Grimm used a slightly different version of the trope in the fairy tale "The White Snake", only this time the lost ring belonged to an unnamed queen and was found in the belly of a duck.
The quote by Nanny Ogg at the top of the page hangs a lampshade on Polykrates' story. it's immediately subverted: after some consideration, Granny Weatherwax replies, "Never. Nor have you." (Naturally, in a later book it actually happens to them.)
Karna from Mahabharata with his father's gift "kavach kundal". He ended up having to cut the thing off his body.
A mild example occurs in The Dark Crystal. Jen throws the Crystal Shard away into a dark swamp at night. That should be one very lost shard. But the next morning there it is, far less than a stone's throw away from where the heroes have slept.
In the Suspense episode "The Pasteboard Box", a man murders his twin brother in order to take his place, dismembers the body to dispose of it more easily—and then just can't get rid of the pasteboard box containing the head. Until the end, when the police show up to arrest the other twin for murdering his secretary. He tries to prove his true identity by showing them his brother's head, and opens the pasteboard box to find that he did manage to get rid of the head after all, and this box only contains the fishbowl he ordered earlier.
The obscure fantasy game Dragon Warriors featured Vallandar's swords in the first adventure. Vallandar was the universe's King Arthur-equivalent who would return to his kingdom at the end of the world, and anyone who took one of the swords (they were just standing there) would have it with them forever so that they could join him. Bury it in the woods, drop it in an ocean, and a few days later it would return to your inventory. These were good swords though, and would even become magical if the player played his cards right.
The Loadstone: Weighs down the user, decreasing his base speed, and appears in one's possession even if destroyed.
The Talisman of Zagy: When used wrong, it acts like a loadstone. But in a subversion, not only CAN you destroy it, but it turns into a diamond if you hold onto it for a few months.
Many cursed weapons (e.g., the ever-popular sword -1) will appear in your hand every time you enter combat, forcing you to use a sub-par weapon. Players quickly found clever uses for this item. After all, you can never be disarmed and never have to carry a weapon when you're "cursed" with the sword. Fighting with a -1 weapon is far better than fighting with no weapon.
In one Paranoia module, the PCs are ordered to dispose of a trash bag full of treasonous Communist propaganda pamphlets, which prove to be indestructible (and if they just ditch it somewhere, then someone ends up finding it and returning it to them). Eventually, they get the pamphlets superglued all over themselves (though this does at least let them survive a massive weapon blast just before the final confrontation).
In Exalted, a Lucky Rock is an otherwise ordinary stone that always reappears in its owner's possession. Simple (but expensive) magic can transfer this quality to javelins, arrows, and other tools of war. The effect is not immediate, so a "lucky arrow" is not a bottomless quiver in and of itself, but the enchantment has obvious utility regardless.
Geist: The Sin-Eaters: Each Sin-Eater has a Keystone Memento, an object that exists partially in Twilight and represents the Bargain they struck with their geist. It can never be taken from the Sin-Eater, and if it is, it just disappears and reappears the next time they call on it.
The Soul Reaver of Legacy of Kain, as his "symbiotic weapon", becomes forever inseparable from Supporting Protagonist Raziel once he obtains it — more so in Defiance, where it serves as the only weapon he and Kain ever wield.
A recurring hazard of many fantasy roleplaying games (both pencil-and-paper and computer/console) are cursed magic items which not only carry some in-game penalty but which force the cursed character to continue using them until the curse is magically removed.
Cursed items in NetHack and most roguelikes will weld themselves to your hand — if you have the misfortune of trying to use a two-handed cursed sword or a cursed sword and a cursed shield you'll be unable to cast spells or use most of your inventory because both your hands are attached to a chunk of metal. There's also items like Nethack's loadstone, which begins doing this the moment you pick it up — it cannot be removed from your backpack in any way until its curse has been lifted and weighs more than most full suits of body armor, and more than the entire weight that some weak characters can carry without being slowed down by the load. And heaven forbid you make the mistake of wearing a cursed blindfold...
There's a few of such undroppable cursed items in Eye of the Beholder II: The Legend of Darkmoon. However, getting rid of them just require one "Remove Curse" spell, which is accessible to both mages and clerics. So it's only a problem if your characters are too low level to cast it (or can't rest and regain spells, but then you have a much bigger problem on your hands).
Cursed artifacts in Planescape: Torment cling to the wielder (like a toothy ring) once (s)he equips them and can only be removed via a cleansing spell. In their defense, they usually offer good buffs so you will only want to get rid of them if you find a something even better for the respective slot. This was true for most cursed weapons and equipment in Infinity Engine games. The difference about it in Torment was that relatively few of the "cursed" items had a downside other than it being impossible to remove them. The true Clingy MacGuffin of the game, however, was Moridor's Box, a quest item that can't be removed unless you give it away, open it, or leave a specific area without completing the quest.
Some of the medium-high bracket of weapons and armour in Golden Sun are cursed, which means when you put them on you cannot take them off again unless you go to the games' resident healers and pay through the nose for what can only be described as "curse solvent". Also cursed weapons have a habit of paralysing you for a turn in battle.
Medium-high for the second game, at least, but the cursed items in the first game were the strongest you'd get, or at least, strong enough that you'd want one of your characters to use them (along with the Cleric's Ring, which nullified every part of the curse except the inability to take them off.) The only reason not to have them is that it prevents you from "fixing" the Random Number God for the item drops.
Same goes for the Dragon Quest games. Once you equip a cursed item, you cannot remove it unless you go to a healer. It may appear to be a high-end weapon, but only give a lousy change in stats.
The Keyblade in Kingdom Hearts is a benign example of this trope. In fact, its inability to leave its user was used as a plot device, as Sora gave it to Captain Jack Sparrow as payment — and it naturally reappeared in Sora's hand later. Said inability is also used for one of the attacks in series; who needs a boomerang when a thrown weapon will unerringly reappear in the wielder's hand, no matter how many times he throws it at an enemy? It's used in a similar way when Roxas tries to disarm Sora by pinning one of his own keyblades into the ground in the handle. It returns Sora's hand, Roxas gets confused, and Sora deals a fatal blow.
It can however be passed to another worthy wielder so long as the original doesn't object and call it back to them. Sora and Riku repeatedly wind up holding each others Keyblades during the Xemnas battle. Also if a keyblader is in self doubt ala Sora thinking he wasn't really accomplishing anything, then another keyblader with stronger convictions can actually steal it until they get out of their funk. Sora, Riku and Roxas have stolen Keyblades from each other and stolen them back throughout their various battles when one of their heroic resolves wavered. Lack of confidence can even lead to the wielder being unable to call the keyblade at all, though Xion can still use Roxas' own effectively when he lends it to her.
Anything designated as a "plot item" in all of Neverwinter Nights is undroppable and unsellable and un-give-to-party-members-able. You are stuck with it. For example, you can't get rid of the Relic of the Reaper in Neverwinter Nights: Hordes of the Underdark. At least, not until Mephistopheles, who bound it to you, takes it from you in person.
The 27 True Runes of the Suikoden series. The True Runes are effectively the gods of the Suikoden world, but they (usually) can't do much without a human host. While the hosts can exercise varying degrees of control over their Runes, it's almost impossible to get rid of them. The Runes chose their own hosts, and also choose when (or if) they leave. Typically that only happens when the host dies, which could take awhile because immortality is one of the side effects. If the host would prefer to live a normal life and die eventually, but doesn't want to die now...that's just too bad. There are very few methods of removing a True Rune against its will, and they either result in either a drastically reduced lifespan (as in, death within a matter of days) or a Fate Worse Than Death, both of which can only be averted by taking the Rune back. And sometimes not even death is enough for the host to escape; at least two of the Runes are confirmed to have absorbed the souls of their prior hosts.
The self-replicating, seemingly-useless artifact known as the "si" from Ancient Domains of Mystery can cause major problems if a player tries running the Infinite Dungeon while carrying it. Extra sis can't be ditched inside the Infinite Dungeon, and the artifact will copy itself, over and over, until the player finds himself crushed under the weight of hundreds of them.
RuneScape has a minor variant of this to keep players on their toes — sometimes a Strange Old Man will pop up near your character, give you a puzzle box, and disappear. This box can be solved for a small reward, but cannot be dropped or banked. What's more, if you don't solve it quickly the box doubles itself, taking up more inventory space until there is none left. Each box then has to be solved individually to make it go away, but you only get a reward after the last one is solved.
Bethesda appears to have fallen in love with this trope as of The Elder Scrolls IV: Oblivion. Any item marked with a hidden "quest item" flag is undroppable without console commands. Even trivial notes and useless doodads can become perpetual inventory clutter if a bug causes the quest flag to not be removed when the quest ends. Although there was a mod for Oblivion that let you toss quest items. Amulet that you need to beat the game? Nope, tossing that in the river!
There was a minor sidequest that dealt with a staff that had an actual magical reason that it couldn't be gotten rid of. This woman found the staff that, when she tried to cast a spell with it, ended up causing a whole bunch of non-hostile scamps to appear and start following her around (the staff was an artifact of Sheograth) She couldn't bring herself to get rid of the staff due to the enchantment, but her friend learns that if someone willingly takes the staff from her, then the curse would transfer to them. That's where you come in... (Don't worry, the end of the quest is you finding a way to permanently get rid of it.)
Fallout 3, being made in the same engine, carries on this convention.
The series iconic Pipboy 3000 is also a canon form of this. This wrist mounted computer is nigh indestructible and can't be separated from its host (voluntarily or involuntarily in most cases). This is taken to ridiculous extremes at times: the Brotherhood outcast sawed a vault dweller's arm off to try to get his Pipboy, but the device wouldn't work afterwards.
In MM3 the quest items appeared normally in the inventory but could not be dropped or sold.
In MM4-5 they never show up in the regular inventory, but had their own section and could not be manipulated in any way. MM6-8 followed the traditional version of this trope, where after dropping a quest item somewhere and then going to talk to the Oracle the item would reappear in the party's hands.
Clash of Heroes brings us the Blade of Binding, which fuses with the users arm.
Sword Of Vermilion has the cursed Dark and Death Swords. If you equip either one, you won't be able to unequip it or cast any spells.
You realize with horror that you are totally unable to put down the Dark One Sign here. It seems to have a will of its own.
The Pyrite Parrot of Petaluma in Tales of Monkey Island, which survives being molten and keeps coming back to Guybrush Threepwood.
In Banjo-Kazooie, collecting the Stop N Swop items will cause them to stay in your inventory forever. You cannot get rid of them, even if you delete your save file. You can, however, get rid of them if you are playing the XBLA version of the game.
In The Clue Finders 4th Grade Adventures, Joni gets an ancient Egyptian ring stuck on her finger, which doesn't come off until the bad guy's goons use a magic spell to attract it. Said ring turns out to be the key to releasing Set.
The dead fish in Space Quest 6. It's confiscated twice from you. First, when you're captured by the Big Bad's Mooks. When you teleport away, one of them throws it back to you ("Here's your fish!"). The second time is when you are capture by the security personnel on the DeepShip 86. When you escape on a stolen shuttlecraft, a bunch of Imperial stormtroopers show up, one of which throws the fish into the shuttle's engine with the same words. Subverted in that the fish turns out to be quite useful in the end.
Link and Zelda are stated to have had parts of the triforce with them all along. In The Legend of Zelda: Ocarina of Time, this forces Zelda to disguise herself as Sheik to stop the Big Bad from getting it, implying that there's no way to just remove it and hide it somewhere. In Link's case, this is implied to be the reason he's the one who has to go on the quest to save the world.
The Book of Claws in They Bleed Pixels has been confirmed to be immune to burying, burning, and dumping in the river with chains wrapped around it. It may or may not be intelligent, but it can almost certainly teleport.
Kurt from Unlimited Saga has a cursed gaunlet which he can't take off. If you play as him, Kurt will be forced to fight one-on-one with a monster from time to time.
In one Rooster Teeth short, Geoff experiences this trope with a box he stole from the Devil in a dream — it was on his chest when he awoke, throwing it into a dumpster only causes it to leap back out, and in spite of leaving it at home that morning, it was sitting on his desk when he got to work.
Blinker Stones from Gunnerkrigg Court are a rather benign variety. They can be retrieved from anywhere with a thought, even if you don't own the stone, though it's not clear whether one can be taken from its owner using this method.
The Necklace of Septumet in the currently defunct comic For Your Eyes Only not only had a difficult to control (and undesirable, at least for the current wearer) power, but it transforms into a tattoo when put on, making it irremovable.
In Full Frontal Nerdity, Lewis has a cursed 20-sided die that is every gamer's nightmare; it always rolls a 1. The gamers give is a burial, but it returns. They bury it again, this time under a statue of the Virgin Mary, with a bunch of garlic. It returns again. The characters decide to de-curse it by mixing it with some dice that are extra lucky — they rolled every die in their gaming store and bought the ones that came up as 20 three consecutive times. But after doing this, all the dice start rolling 1s. ("It's like we tried to cure a zombie by locking it in a room with normal people!") Then the other cursed dice vanish, and the number 1 starts appearing world wide — sports all end up with a score of 1, clocks stop at 1:11, etc. The gamers decide that the only way to break the curse is to make rolling a 1 good. Fortunately, Nelson had the foresight to buy a lottery ticket with all 1s, and won $1,111. They use this money to bribe Wizards of the Coast to temporarily change the rules of Dungeons & Dragons so that 1s are good (version 1.1.1 — their word processor was cursed too). Lewis rolls the die in the hopes of getting a 1 and lightning strikes, destroying it.
Also SCP-1015-1, which only switches owners if taken without permission, or the owner is killed.
The Amulet of Cthon from the Global Guardians PBEM Universe. Putting it on makes a person utterly invulnerable to attack from forces both mystical and scientific... and slowly causes the user to become obsessed with the Great Old Ones, to the point that within a couple of years, the wearer is an utterly invulnerable cultist devoted to bringing the Old Ones back. And it won't come off until the wearer dies...
In Noob, Sparadrap's cheated staff (and presumably similar objects Tenshirock introduced into the game) can't be deleted by normal means and will be part of the Starter Equipment if its possesser get banned by a Game Master and creates a replacment avatar. It's actually so clingy that the Game Masters settled for getting it Brought Down to Normal the second time they ran into it.
The Omnitrix in Ben 10 can't be removed without incredibly specialized equipment, skills, and technical knowledge — and a whole lotta pain. You could also kill the person wearing it or cut off the limb that the Omnitrix is attached to. Naturally, the Big Bad tries this but is thwarted by the good guys before he gets the chance to hack the boy's arm off. Oddly, in the What If? episode where Gwen gets the Omnitrix, the Big Bad indicates that he could remove it a lot less painfully (though Gwen hadn't been wearing it nearly as long), but wants to hack it off anyway For the Evulz.
Subverted in the immediate sequel, Ben 10: Alien Force. The series finale reveals that Ben has learned how to remove the watch himself using a voice command and Override Command, so it's not technically a Clingy MacGuffin anymore. It gets destroyed before the episode ends, and it's currently unclear if his new Ultamatrix is clingy or not.
Another episode has our heroine donning a pair of red shoes that will allow her to move at hyperspeed to keep up with all her responsibilities. Unfortunately, once again they work too well, as they become stuck and won't come off her feet. For the rest of the episode, Kim (and Rufus, who also had a pair made for him) are stuck moving at hyperspeed, and at the end of the episode they're still wearing the shoes. Kim eventually Hand Waves this by assuring Rufus that the shoes will probably come off... eventually, anyway.
Aqua Teen Hunger Force. Two undying, self-mobile dummies (voiced by Josh Homme of Queens of the Stone Age and T-Pain) plague the household. Smash them, bash them, they just return. Shake, in an odd moment of logic, uses them to create a profitable magic show. Turn one into splinters, it just wanders right back out from behind the curtain.
Sabrina: The Animated Series has Sabrina getting a pair of magical dancing shoes for her boyfriend Harvey when he confesses that he can't dance. Unfortunately, the shoes work too well, as they won't come off Harvey's feet and force him to dance whenever he's in the vicinity of music.
Played for Laughs in an episode. The family goes on vacation to Hawaii and Candace finds a Tiki necklace that seemingly curses her with bad luck. She tries to get rid of it, but it keeps coming back to her. It later turns out the Tiki necklace was a restaurant gimmick, and earned her a free dessert, which she turned down.
And then there is the episode that parodied The Wizard of Oz. When the Wicked Witch (played by Dr. Doofenshmirtz) demands that Candace hand over the magic red-rubber boots, she replies that she would, but they've grown on her. By that, she means that thorned vines have literally grown onto her legs and they won't come off. It's only after Phineas and Ferb give her a red-rubber shoehorn that she's finally able to remove them.
One House of Mouse short was actually about Mickey Mouse having a hard time sleeping because of his new alarm clock's ticking noise. He always tries to get rid of it, but no matter how hard he tries, the clock will inevitably make its way back to his house.
The Green Shoes in the Looney Tunes cartoon The Wearing of the Grin.
The Alicorn Amulet from the My Little Pony: Friendship Is Magic episode "Magic Duel" is a variant of this trope: it can be removed, but only by the wearer. Since it grants immense magical powers to the wearer (Trixie in this episode), they will have no desire to remove it, but it also makes them evil, so the main characters have plenty of reasons to want her to remove it. They succeed in making her remove it by tricking her with an even more powerful (but fake) amulet.
In Captain N: The Game Master we find out that Princess Zelda was now connected to all three Triforces. When Eggplant Wizard and King Hippo steals two of the three Triforces, she's brought to the brink of death and Link and the N-Team have to hunt down the missing items.
This can happen to people who wear the same ring for too long, such as a wedding band. Over time, a person's fingers can develop around the ring to the point where it becomes stuck and can't be removed without filing it off. It's common enough that specialist tools exist just for removing such rings.
Glitter. Try getting it off you.
Pet hair. Especially when you're wearing black.
Fine sand, especially from the beach. You'll find sand in places you never know could be possible.
Credit history, criminal records, educational records, and a myriad of other records collected by the government and private industry tend to follow, and potentially haunt, a person until they die. Or longer.