Ancient Sins: After the defeat of The Nothing/Tadmir, Dante is cursed with Complete Immortality. Meaning he can't be killed by anything, even other immortals. This is done purely to torment Dante by making him witness everything he loves die. He does manage to find a way to rid himself of this, after everyone is dead, and proceeds to do this. Discord, being the only other fully immortal being in the universe, also joins in on this and the two die from all their years catching up with them.
The fic Circle of Friends has this as the whole theme. Princesses Celestia and Luna abdicated to Twilight Sparkle so they could die, then she allowed her friends to live as long as they wished to, they lasted a couple centuries before they could no longer take it. At the end Princess Twilight is training her successor so she can join her friends.
Celestia and Luna have been around for more than four hundred million years, created and witnessed the extinction of entire species, and have near perfect recollection of everything (except that Celestia can't remember ponies' faces and Luna can't remember ponies' names). Despair is a frequent threat to them, but ultimately they decide to soldier on because they have no choice.
Played very straight with the original alicorns, and the reason for their extinction. They were immune to age or disease but still died from accidents or violence, except they didn't have near-perfect memories, meaning they eventually forgot their dead loved ones but still kept the pain and grief, now with no idea why they felt this way. It eventually drove them insane and they started slaughtering each other.
She holds this view, even as Cadence and Luna point out the common reasons for this trope (loved ones die around them, no one else understands immortality, is forced to remember every event of their lives, both good and bad, boredom, etc.) do not apply to alicorns. Does not stop Celestia from giving suicide the old college try though.
It's explained by both Luna and Cadence that this happens every few centuries and it's just better to let her get it out of her system.
The Great Alicorn Hunt is a response to all the "immortality sucks" fics. According to Celestia and Luna the idea that one would get "bored with life" is ridiculous and Malthus was an idiot. The only thing that makes it heartbreakingly painful for them is the whole "outliving your loved ones" bit, and they're working on that by trying to make everypony else immortal.
In It Takes a Village, Spike is not happy about his projected lifespan, although Princess Luna did provide some perspective along an offer of friendship. On the whole mostly averted once Spike decides that by living as long as he will he can keep the memories of his friends alive for their descendants.
Brought up in the cases of Spike and Celestia in Last One Standing, who are doomed to outlive everyone they know.
The Petriculture Cycle: Discussed and averted in π. Not only does Penumbra not put any stock in this trope, it turns out that it isn't even applicable. Alicorns aren't actually immortal; they just "don't leave until they're ready to go."
Later in the story, Marcus realizes that he (and possibly also Cheerilee and even Lyra) could have their own ascensions as well, making him fear the possibility of suffering this. Luna reassures him that as long as he has fellow immortals alongside him, he (and by extension anyone else in the same boat) won't be alone.
In The Jewellery Box, Spike mourns the loss of his friends because they died hundreds of years ago. His desire to have them back is what triggers his greed growth again, but because he feels he can never really have them back he retains his rational mind.
In Twilight Then, Twilight Now Universe, Applejack has been immortal since the first fall of Tambelon. She continuously regrets that she ever became immortal. Admittedly, a large part of this is the fact she has lived through multipleGotterdammerungs and watched her beloved home pushed to the brink of annihilation, only to survive by decaying into a Crapsack World, which has left her rather... broken.
Explored with in Within And Without as Luna comes to terms with her past mistakes. It's also revealed that the Elements of Harmony grant their bearers the choice of immortality.
This fancomic suggests that "Immortal Twilight" fics go one of two ways. If the author is 20, she gets all Wangsty. But if the author is 30:
In Forever Young, Discord has cast an immortality spell on Fluttershy so he wouldn't have to outlive her. Problem is, Fluttershy doesn't want to outlive her friends either. Discord offers the same spell to any of her friends, but Fluttershy asks Rarity and realizes they all have friends and loved ones they wouldn't want to leave behind. Discord ends up secretly casting a mortality spell on himself - when Fluttershy ultimately dies of old age, he's not far behind.
Starswirl was an immortal unicorn who, after several centuries, felt weary of his extended lifespan. Eventually he found a replacement and transferred his immortality to her.
Astelle was given Starswirl's immortality but ran off after he rejected her love. She came back afterwards mainly became she didn't want to be immortal if they couldn't be immortal together. She takes it poorly when it's revealed that Starswirl "cursed" her younger sister Celestia (and their younger sister Luna) with the same immortality. A thousand years later, Astelle's immortality is broken when she's Brought Down to Normal and turned back into an Earth pony.
The Avengers fanfic Lazarus' Daughter, about a girl whose father gives her a serum that provides immortality. In chapter 16 she gets access to a vial that could cure her and questions all the things she misses out on as an immortal
There is a Ranma ½ fanfic in which Cologne thinks to herself about her long life. Pretty much it boils down to 1: After the first three centuries it starts to get rather boring. Two: Everyone finds a clutch. Cologne has managing her village, Happosai has liquor and women, and another one that she heard about is trying to play every Go match he can find. And finally Three: That Clutch cannot turn into your only reason for living. Happosai is unbearable and the Go player has only been seen out of his cave once in the last century because he needed a new Go board.
Bag Enders doesn't really explore this much, but since the Fellowship are now over six thousand years old and have been having embarrassing misadventures together for most of that time, one wonders if their immortality is really a reward for saving Middle-earth or a punishment.
The Wicked fic Never Die explores the real meaning of Elphaba's spell on Fiyero, specifically the never die part and the fact spells cannot be reversed, it sets this troper off in hysterical tears every time.
The The Legend of Zelda fic Eternity features a Big Badwho achieved immortality and is trying desperately to die, even if it means destroying all of Hyrule in the process.
One Ecco the Dolphin fanfiction had the eponymous dolphin endure immortality, outliving his family and friends, watching species pass into and out of existence, and even getting to see the sun swell tremendously within the span of his long, long life. He eventually attempts to kill himself with the incredible pressure of the deep ocean, ending in something of a Mind Screw in that he somehow finds the surface of his youth, friends and all. It then cuts to Ecco's dead body, very old by dolphin standards but hardly immortal, and two young dolphins commenting that he'd been off in his own world for most of his old age.
Touhou Ibunshu, as a Dark Fic of Touhou, naturally has characters that were originally on the Living Forever Is Awesome side of things take a turn closer to this trope. Mokou is the most spectacular and insane example, having lost her mind completely a long time ago (she claims to have spent a decade or so experimenting on interesting ways to kill herself), but the most altered from the original is Yukari, who is so utterly bored of being confined to the same old Gensoukyou for centuries that she decides to obliterate Gensoukyou entirely, which would finally give her a chance at being free.
The theme continues all the stronger into the last story of the series, featuring Kaguya, Eirin and Mokou, three immortals of a different variety than Yukari. The climax of the Final Battle with Mokou has the Phoenix appearing and offering the three the ability to die, either right then and there or after aging naturally. Mokou takes the first option, while Kaguya and Eirin opt to continue on together till the end of time.
In Travels Through Azeroth and Outland, the undead narrator isn't worried about this, because he's pretty sure he'll be killed exploring some hellhole before the endless years get to him.
In A Hero, a crossover between Doctor Who and Puella Magi Madoka Magica, after it is revealed that Puella Magi don't age, Madoka starts to worry immensely about Sayaka falling into this trope. Though Dalek Sec has been around for a quarter of a billion years from his perspective, and sees it as good thing, so he could give pointers as to how to deal with it.
The Sailor Moon fic A Seedling Among The Ashes has Makoto deal with it since by the time the Sailor Senshi gain their immortality she is already married with two kids. It does have a happy end though.
The Hetalia: Axis Powers AU 1983: Doomsday Stories plays with the idea in the case of Austria. While he was eventually able to shrug off, albeit with difficulty, the chaos of Doomsday, his denial of Hungary's death until several years later proved to damage his sanity. Fortunately, things do get better. But had Hungary not shown up, he would have spent the rest of his life in perpetual grief, if not turn into a deranged Yandere.
Elsa has this to a degree in "Lady in White: Legacy", although she prefers to think of herself as just staying the same while everything changes rather than consider herself outright immortal; she doesn't 'want' to die per se, but mourns how she has outlived her original friends and her sister, and had to witness her nephew being killed during an anti-royalty revolution (that she believes was provoked by outsiders) and focus on protecting his children at his request.
In Harry Potter and the Methods of Rationality Dumbledore holds this position believing death is the start of the next big adventure and genuinely doesn't understand why anyone would even think about immortality. Harry explains that while Dumbledore believes in an afterlife, not everyone does and for them, death would be his equivalent of the destruction of a soul.
Artie: Live. With all the death and crazy and losingwell almost everyone. Why aren't you crazy like the rest of them?
Griffin:(long pause) I mourn, I suppose. I mourn for my wife everyday, and now for my child and my grandchild who I will never meet. But-what can I do? I can't change what has passed any more than I can stop the waves from comin' in on the seashore. I'm only a man.(brief pause, then he smiles faintly) I've made mistakes, Christ, we all 'ave. We tried to play at bein' God. It was arrogant and foolish and we thought we succeeded. We forgot that God is lonely. Why else would he have made man? Its not the age or the grief or the rage. Its the loneliness that has driven all of us mad. We cling to the people around us, to save us from ourselves. And when they die, we can't follow. After a while, the options become either cut yourself off totally or go completely insane.
Artie: What about you?.
Griffin: I've realized that I can't fight the tide. I'm just floatin', is all. Does that answer your questions Agent Nielson? Or do you want to listen to an old man reminisce some more?
Timothy Neogene/Timmy Turner in the The Fairly OddParents fanfic series Burning Black. Timothy's immortality can let him survive anything, which isn't as cool once one thinks about what that really means.
In the AUXiaolin Showdown fic Demon of Wind, Guan and The Bird of Paradise discuss the implications of this. Guan's been around for 1500 years and The Bird of Paradise hinted to be at least a millennia.
Certainly the case for Vivio of the Lyrical NanohaAU fic The Bitter End, who has probably the longest lifespan of the cast, with projected lifetime outpacing everyone else's by as much as half a century.
In the Naruto fanfic Gender Confusion, Hidan begs Jashin to set things right and remove his immortality so he could die with his beloved. Jashin obliges.
In the Invader Zim fanfic My Hostage Not Yours, Zim warns Gaz about this when he gives her a pill that slows down her aging process so she would live as long as he does, but she doesn't really start thinking about the ramifications until afterwards. This then becomes a moot point when she gives Dib the pill as well, so she won't be outliving him.
In the Adventure Time fanfic The Last Human, while not a particularly prevalent theme in-story, as Marceline's attitude seems to lean more towards Living Forever Is Awesome, a rather nasty moment from her is revealed to be the result of her father trying to convince her that trying to romance Finn is a bad idea, alluding to his own time with her mother. She and Finn make up, but she implies a fair bit that her inevitable outliving of Finn and their friends is a source of a lot of grief for her.
In Transformers Alter Verse, a few of the Transformers feels this way, but most of them are pleased with their state of semi-immortality. The Seraphims have to live with it, as most of them are immortal or at the very least semi-immortal.
Subverted in the Dirty Pair fanfic Undocumented Features — his loved ones decide to get the immortality treatment as well. Then the people who care about them, until every single Wedge Rat is immortal. As are their descendants.
Played somewhat straight in Aegis Florea 2 when Sumire is revealed to have, as a result of a combination of this Trope, Victory Is Boring and her own unrequited love for Gryphon, spent the previous forty years in the throes of a Heroic BSoD until Kei reboots her with a What the Hell, Hero?/"The Reason You Suck" Speech that is so scathing and insulting that she cannot help but to rouse from her self-imposed emotional stupor and get angry.
Porky in the Super Smash Bros. fanfic What Goes On doesn't seem to have a problem with it, but everyone else can clearly see that it's not a great state to be in. And the only reason he bugs them is because he's bored, a major complication of this trope.
The Twilight fanfic ''Revelations'' has Bella realize some time after Breaking Dawn that immortality and being a vampire is not what it's cracked up to be for the usual reasons of this trope (friends and family all die, boredom, etc) as well as come to realizehow terrible she was towards her human friends and family and wishing desperately for a second chance to make things right. Carlisle himself also admits that he sometimes wishes he could pass on, only staying alive for the sake of helping others and being there for his family.
In Forever is an Exceedingly Long Time Harry, unable to locate one of Voldemort's Horcruxes, feeds him Draught of Living Death and leaves him under a stasis charm powered by his own magic. He wakes up some two and a half billion years later on a wasteland of a planet with nothing recognizable as humanity, only to be faced with another two and a half billion or so until the sun goes nova.
Hinted at in the second Weasley Girl story, Secrets of the Past, where Veronica "Ronnie" Weasley overhears Dumbledore and Nicolas Flamel talking:
Dumbledore: I am glad you and Penerelle decided to remain among the living for a while longer. Your advice has always helped me greatly... and I do think that, with Voldemort still out there, the world might still need you. Flamel: The world will always need us. Always there will be some new catastrophe, some new evil to be defeated, some new problem that needs to be solved. When will it end? When are we allowed to rest?
Sailor Moon: Legends of Lightstorm: While Sailor Jupiter seems excited about living forever, Jason seems unenthused about it. Granted, it may or may not have something to do with losing his powers, since all Sailor Scouts and Justice Champions are biologically immortal whether or not they transform.
The Sanctuary Telepath: when Janine snaps she tells Ranna that she consented many things in her life (including her own mental torture and injecting vampire blood into her veins) but immortality was not one of them.
Brought up in Powers of Invisibility, when Juleka learns, after accepting the Turtle Miraculous, that this will give her an extended lifespan basically guaranteeing that she will outlive Rose. While Juleka acknowledges that this will be painful eventually, the situation Rose is in right now means she can't exactly change her decision.
In Say a Prayer a Gringotts cursebreaker comments that all the Egyptian wizards who tried for immortality became mindless mummies and that the traps in their tombs are as much to keep them in as to keep everybody else out.
Sheldon: Mad revenants, locked away in tombs, in the dark, for thousands of years, because they couldn't be allowed to roam free. If there's any part of the wizards still in them I couldn't tell you. Poor bastards. I'll bet you every last one wishes they'd never even considered it. I very much doubt thousands of years imprisoned in a dark, airless tomb is what they thought of when they decided to live forever.
Escape From the Moon: Late in the sequel The Mare From the Moon, Spliced Genome begins to really hate her immortality. After years of promising to turn her mortal, those in charge admit that they lost the process to render her mortal again. This only furthers her growing depression.
Both oneshots Time Passes and Prisoners of Time revolve around Rapunzel being immortal. Decades pass, Eugene and eventually even their descendants start dying, yet she doesn't age past 18. Rapunzel tries to kill herself but it doesn't work. She spends the next several decades trying to find ways to die, but none work. She doesn't die until millenia later, when the sun finally goes out.
All-but-explicitly stated in the Infinity Crisis story Of Kryptonians and Queens, when Jason Blood notes that Morgana can't threaten him with death as he'd actually welcome it.
Both Tonks and Fleur in For Love of Magic eventually come to regret their immortality due to watching their descendants grow old and die while they stay in their prime. After a few centuries, they stop taking the Elixir of Life and allow themselves to die. Luna chooses not to because doing so would leave Harry alone.
In the sequel, Harry admits that he and Adrastia are fine with eternal life because they're both sociopaths whereas Luna can handle it because she's mastered living solely in the present. On the other hand, Harry's new mortal wives start drifting away from him as they age due to not wanting to be reminded that he'll go on living while they wither and die, nor do they want to live while their children die. According to Harry, trying to keep his entire extended family immortal resulted in most of them dying off at once when the centuries got too much to bear.
Xanna (the Nine Tails) carried this belief for a long time in Reaching for a Dream due to her loneliness. Once she and Naruto ascend to godhood, her attitude changes to Living Forever Is No Big Deal out of faith that when they get bored with eternity, Naruto will find a way to kill them both.
In Empath: The Luckiest Smurf, Baby Smurf comes from Smurfling Island, where nobody ages, as also do the Smurflings with the exception of Sassette, who came from a Crystal Prison. It is presumed that whoever lives on that island has their aging forever locked at a certain age, which is why when Baby Smurf first appears in the Smurf Village, he is no more than a day old despite probably being older than that. At first the parents of the child want Baby Smurf be brought back, but after Smurfette's letter being written to them explaining how terrible it would be to condemn a Baby Smurf to living forever without ever aging to become an older Smurf, the parents realize the wisdom in Smurfette's statement and thus allow Baby Smurf to stay in the Smurf Village forever to be able to grow up.
The Disney Princess fanfic Old And Graceful sequel features Meg being distraught that Hercules died before her, so when he sends down a magical flower that gives her youth in order to have a second chance, she misuses its powers so that she lives for millennia. She becomes Mother Gothel when she can barely remember her old name and living for so long, being horribly dependent on the flower causes her to live a miserable existence. By the time she kidnaps Rapunzel it's debatable as to whether she wants to live any more.
The Powerpuff Girls oneshot Deicide is about Blossom having an existential crisis over her invincibility. She can't age over five and is functionally immortal. It gets to the point where she has a breakdown and tries to kill herself.
The Infinite Loops: Loopers are stuck in a random, varying series of time loops, occasionally crossing over with other worlds. There is no escape whatsoever, and the oldest loopers have been going for millions of years. While they typically decide Living Forever Is Awesome eventually, it takes a while. In particular, who is Awake varies with each loop (except for the Anchor, who is Awake for every loop), meaning that often times their closest friends and loved ones will essentially disappear for a few centuries, and they have to pretend everything is fine.
Twilight Sparkle: I think that is the root of a lot of madness among Loopers. Offer Dash nothing? Gilda, she has hope of seeing her friend now, not an endless parade of someone wearing your face that can't remember the real her anymore.