This is the entire premise of The Age of Adaline: the main character stopped aging and has had to live an isolated existence ever since, avoiding close ties to anyone and changing her name every decade to avoid suspicion. She has also had to watch her daughter grow old while she herself has remained the same age. She explains to her daughter at one point that, without being able to grow old together, love is only heartbreak.
Bicentennial Man: Andrew extends Portia's life significantly to prevent her death, but since she doesn't want to live forever, he eventually arranges a way to make himself mortal as well.
Andrew: I've always tried to make sense of things. There must be some reason I am as I am. As you can see, Madam Chairman, I am no longer immortal. President Bota: You have arranged to die? Andrew: In a sense, I have. I am growing old, and my body is deteriorating, and like all of you, will eventually cease to function. As a robot, I could have lived forever. But I tell you all today, that I would rather die a man, than live for all eternity as a machine.
Averted in The Crow: City of Angels: In the original ending the crow was killed, preventing Ashe from returning to the afterlife and leaving him to wander the Earth as an immortal spirit, unable to die. Executive Meddling resulted in a reshot ending where Ashe returns to the afterlife regardless of this and is reunited with his son.
D-F
Daybreakers has shades of this when a virus outbreak changes most of the populace to vampires. The opening of the film see a vampire girl committing suicide by sunlight having written a letter explaining how she'll never grow older. The protagonist of the film, Edward, is also weary of never growing old as well.
In Death Becomes Her, Madeline and Helen drink a potion that grants eternal youth, but it does not protect them from damage to their bodies. Accidents and attempted murders leave their bodies dead and permanently mutilated. On the other hand, Ernest is offered the potion, but he refuses it, because of how eternal life would be a nightmare even if he didn't fall victim to accidents and mutilation (Furthermore, eternal life with only those two rather horrible women for company really would be a nightmare). He ultimately lives his life happily with a large family and dies peacefully, while the two women bitterly linger on, imprisoned in bodies that literally fall apart at the very end.
In The Death of Stalin, Nikita Khruschev warns Maria Yudina that their prior association could be used as a pretext by the secret police for killing both of them:
Maria: Maybe... but I'm confident of everlasting life.
Khruschev: Who the fuck in their right mind would want everlasting life? The endless conversation...
In The Fountain, Tom Creo seeks to discover a medical means to immortality through experiments with the bark of a rare tree, but he ultimately learns to accept death as a necessary aspect of life. Though our bodies die, the material is recycled into new organisms, and so we live on through new life. Even planets and stars that die become new stars and bring new life to other worlds. Two parallel stories feature different versions of Tom achieving immortality and finding it fruitless. Tomas the Conquistador seeks and finds the Tree of Life, but ultimately the sap turns his body into flowers, in something of a Literal Genie ending. Spaceman Tom has apparently succeeded in becoming immortal by consuming bark from the rare tree that was grown from the body of his dead wife, but the tree dies before he can resurrect her in a supernova. A vision of his wife convinces him to accept death with joy, and he dies in the supernova, becoming part of a new star. Interestingly, the story also makes room for a very unsympathetic priest to prattle on about immortal souls, which the film seems to dismiss outright.
The adaptation of Frankenstein, Frankenstein: The True Story has the creature try to destroy itself after it realizes its body has begun to degrade making it ugly and unacceptable to humans. At the end, Frankenstein apologizes for cursing it with an undying body as both are buried in an avalanche of snow.
G-I
Tom Hanks's character in The Green Mile ends up outliving all his family because he receives part of the life force of the death row inmate John's healing power. He believes this is punishment from God for executing John. He's not immortal, though. Death will catch up to him eventually, but not for a very, very long time as seen with the mouse Mr. Jingles.
Groundhog Day involves a man forced to relive the same day over and over again (for a total of 10,000 years, according to the original script). He commits suicide several times and that only makes the day start over again from his perspective. He doesn't let that get him down for long, but instead makes the most of his endless time and becomes a better person.
He Never Died uses this trope as its primary plot device, though the protagonist seems to have gotten used to it after thousands of years.
A core concept of the Highlander franchise, of which the loneliness of immortality plays an important part:
The first three films largely center around Connor MacLeod, a 16th-century Scotsman who finds out exactly what happens when one learns they're immortal - he's stabbed through the chest, is presumed dead, freaks out his nearby clansmen when he revives and is nearly burned at the stake before cooler heads prevail and he's exiled instead. Later on, with a montage set to Queen's "Who Wants to Live Forever," Connor and his wife Heather pass a long and happy marriage together, but Connor must watch his beloved age and die while he lives on, ever youthful. Worse yet, immortals can't bear children, with Heather lamenting this fact just before she passes. By 1985, Connor lives mostly as a recluse, surrounded by antiques, as getting to close to people only leads to risk of his secret being found out, and heart aches when they die. His only social contact being Rachel, a Jewish girl he rescued in World War 2 and semi-adopted, who by this point looks older than he is.
There was a lost sequence (the footage was sadly destroyed in a fire) where the Kurgan fights a Korean immortal named Yung Dol Kim, who is masquerading as a security guard. Kim actually throws down his swords before the Kurgan and just tells him that after 400 years of empty living, he would just be happy to die. The Kurgan, who it bears repeating is an Ax-Crazy barbarian to the nth degree due to centuries of endless violence, is visibly taken aback by this.
In an early draft of the original film's script, it was explained that, were it not for the Gathering (the event that draws immortals together to fight and kill one another), Big Bad Kurgan would never get out of bed. In the final film, he has the same sad, lonely look Connor has, but is otherwise content with his lot in life in 1985.
Never mind the fact that many people will want to kill you. Some because they think the fact you're immortal in the first place means you've made a pact with Satan or are otherwise some sort of Humanoid Abomination; others, fellow immortals, want to kill you because doing so makes them more powerful, and the whole idea of your immortality is that "There Can Be Only One" so all of you will have to kill each other at some point, until only a single one is left. By the way, the only way to kill you is Off with His Head!- the former group probably don't know this, so prepare yourself for a lot of painful non-deaths. Which, it so happens, is how your immortality was activated in the first place - you died a violent death to get it. And you probably didn't know about it until that happened.
In Highlander: Endgame, Connor is one step away from being a Death Seeker, due to having lost countless friends, family members and lovers over the intervening five centuries. It is revealed that Big Bad Jacob Kell has been responsible for many/most of those deaths, forcing Connor to commit a Heroic Sacrifice by allowing Duncan MacLeod to behead him and take his power to use against Kell.
The series also examines marriage with a potential immortal in Endgame. Duncan falls in love with a woman who he believes is immortal, and deliberately causes her violent death (on her wedding night, no less) to activate her immortality without bothering to explain his rationale for doing so. This causes her to quite rightly freak out, run away and become the right hand woman to the guy that wants to kill him.
Hocus Pocus has Thackery Binx cursed to live forever as a cat by the three witch antagonists, forcing him to live with his guilt of being unable to save his sister from them. Conversely, The three antagonists wish to be immortal (it was their goal when they were originally alive, but after being brought back to life, it was the only way to maintain it) by draining the youthful life forces of children.
The premise of Hook is that Peter Pan realized the disadvantages of his eternal youth when he discovered Wendy had grown up and aged into an old woman. Which made him decide to give up his immortality, return to earth, and live a normal life.
Adam, the protagonist of I, Frankenstein, doesn't see his immortal life as a gift. After encountering the gargoyles and the demons, he arms himself with demon-slaying weapons, but doesn't specifically task himself with ending the demons. Instead, he simply goes through centuries, still bitter about his creator turning on him. It's not until the climax, when he finally gains a human soul, that he resolves to use his immortality to protect humanity from the demon threat.
In The Imaginarium of Doctor Parnassus, Doctor Parnassus makes a wager with the Devil, with immortality as the prize. A thousand years later, Parnassus is a broken-down drunk and so miserable that he believes the Devil let him win just to torture him.
In In Time, Henry Hamilton chooses to transfer his remaining lifespan to Will Salas, dying as a result, because he could no longer live with himself knowing that his rich compatriots hoard all the wealth to live forever and let the poor die. He has already lived for a century, while still looking like Matt Bomer.
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In Jungle CruiseFrank reveals he was cursed with eternal life and after centuries plans to kill himself when the curse is broken as he feels he's seen everything the world has to offer. After the curse is broken, Lily convinces him to live out the rest of his life with her.
In The Last Witch Hunter, this is the result the Witch Queen wants to achieve by giving Kaulder his immortality, as this way he'll never enter afterlife to see his wife and child again. He's terrified by this in the prologue, but after eight centuries of Time Skip, he seems to have largely taken it in stride.
Little Big Man ends with Jack Crabb alone once again, pondering how he has outlived everyone he knew.
The One Ring's ability to grant an extended lifetime to its bearer has, in the literature, been considered a curse on its own, particularly in regards to what it did to Gollum. When Bilbo Baggins finally and willingly gives up the Ring (with some reluctance), he steps out of his house, seems to shake off the discomfort, then tells Gandalf that he's figured out an ending for his book- "And he lived happily ever after, to the end of his days." It's a very encouraging sign that the first thing he says after giving up the One Ring, is the comforting notion of living, and dying, peacefully.
Théoden's battle cry "DEAAATH!" seems a less ironic version of the above-mentioned "Do you want to live forever?" because it pretty much points out that death what is what they are all heading for. Points in favor: (1) Instead of being disheartened, the Rohirrim join in and throw themselves into battle, (2) Tolkien's idea of death as a gift.
Arwen definitely has shades of this, because if she lives forever she will be parted from Aragorn, who is mortal.
M-P
In the 1940s German adaptation of Münchhausen, the storyteller of the framing narrative is revealed to be the baron, who loves his present wife of fifty years so deeply that he decides to relinquish his immortality to die with her, aging to her exact age before his guests' eyes.
Count Dracula: Time is an abyss… profound as a thousand nights. Centuries come and go. To be unable to grow old is terrible. Death is not the worst. There are things more horrible than death. Can you imagine enduring centuries, experiencing each day the same futilities?
The Old Guard, a film about a small squad of immortal Hired Guns, has this going at least with two of the characters. It's this feeling that prompts Booker to betray the group - even though as a French soldier from Napoleon's armies he's the youngest immortal by many centuries, he still outlived all of his sons and watched the last one die of cancer at 42; he becomes convinced that modern science can discover the cause of their immortal condition and - as he hopes - end it. Andy, the oldest immortal by far, is so old that even she has forgotten what culture she came from, what her original name was and what her family looked like, and she is deeply bitter and cynical about dedicating millennia of heroic deeds to humankind and watching the world get worse and worse anyway, and it takes seeing Copley's conspiracy wall and how the immortals' actions have benefitted the world that causes her to change her mind.
Not the case however with Joe and Nicky, two 11th Century warriors who found each other during the Crusades and fell in love. Even a thousand years after first meeting, they're stillSickeningly Sweethearts.
Lady Aone in Onmyōji (2001) laments how meeting people always means seeing them die as well. She gives up her life at the end of the film to resurrect Hiromasa and is then able to reunite with her lost love.
It seems ("Why are these things never clear?") that whoever stabs Davy Jones's heart will have to live forever, ferrying souls to the afterlife and being allowed to step on land only once in 10 years, or, if you don't ferry souls and skip out on your job, turn into a fishman. Davy Jones is depressed/angry, Will is willing to do it despite leaving his fiancee, and Jack Sparrow thinks it's freaking awesome, complete with an internal debate over whether one lifetime with unlimited rum access or an unlimited lifetime with rum every 10 years is more rum.
The first movie, Pirates of the Caribbean: The Curse of the Black Pearl, revolves around Barbossa and his crew trying to recollect all the cursed Aztec gold they stole. They're cursed with Immortality, except that food and drink is tasteless and they are constantly starving.
Barbossa: For too long I've been parched of thirst and unable to quench it. Too long I've been starving to death and haven't died. I feel nothing. Not the wind on my face nor the spray of the sea. Nor the warmth of a woman's flesh.
At the beginning of Pirates of the Caribbean: Dead Man's Chest, Boot-Straps Bill Turner tells of how he, still cursed with immortality by the Aztec gold, was turned upon by the crew and left at the bottom of the ocean. Naturally, Davy Jones offers him an escape from this and he takes it.
Teague: It's not just about living forever, Jackie. It's about living with yourself forever.
In Pirates of the Caribbean: On Stranger Tides, it turns out that Blackbeard is the only character who honestly wants the Fountain's promised immortality for himself. Angelica wants it to prolong her time with her father; the Spanish want to destroy the Fountain, to protect God's exclusive right to dispense eternal life; King George's men, not realizing this, want to stop the Spanish king from claiming immortality; and Barbossa really only wants revenge on Blackbeard. Even Jack decides he'd really rather be remembered forever than become immortal due to Human Sacrifice.
Jack: "Oh, it's a pirate's life for me. Savvy?"
In the film version of Queen of the Damned, this is the driving force behind Lestat's actions, and thus the entire movie.
"Immortality seems like a good idea, until you realize you're going to spend it alone."
Q-S
The 1985 film from New Zealand, The Quiet Earth, is about a man who finds himself the only man alive after an experiment he participated in to change the universal constants, except for two other survivors he later finds. He insists at one point that he can't die. And indeed he becomes the only one left alive, despite attempting at self-sacrifice, stranded in a universe which has had its physical laws rewritten.
Razor Blade Smile has a common subtext about how a vampire can come to terms with living for centuries. By the end of the main plot it turns out that the entire conflict was exactly this, a game to while away the centuries with living pieces.
RoboCop. When Dougy warns Emil that smoking will kill him, Emil sarcastically replies "You want to live forever?"
Shadow of the Vampire. Count Orlock reads the book Dracula and is saddened by the scene where Dracula leaves a meal for Jonathan Harker, and remembers when he used to have servants to do such tasks for him, which reminds him of when he had a wife, family, estates etc, whereas as now he's just a bloodsucking scavenger living in a ruined castle.
"He has to feed him, when he himself hasn't eaten food in centuries. Can he even remember how to buy bread? How to select cheese and wine? And then he remembers the rest of it: how to prepare a meal, how to make a bed. He remembers his first glory, his armies, his retainers, and what he is reduced to. The loneliest part of the book comes when the man accidentally sees Dracula setting his table."
When the title character of Skellig is told he looks like a dead person, he very seriously replies, "I should be so lucky." He has completely given up on life, but says he is thousands of years old and is heavily implied to be an angel, so death is not even an option for him.
Spring: Louise at first claims she loves her immortality, and nothing is good enough for to give it up. Evan though says being mortal makes life more precious, since every moment counts more with them being more limited. Louise appears to agree with him at the end as it's implied that her love for him made her become mortal.
T-V
The 1990 short film 12:01 involves a man who encounters the destruction of the entire universe when it collides with another universe. But the process in fact sets the time back an hour. And there's nothing he can do to save the universe. So he lives the final hour of the universe, forever.
Torture Garden: In "The Man Who Collected Poe", the resurrected Edgar Allan Poe finds his resurrected existence unbearable as he had welcomed the sweet embrace of death.
In Troy, Achilles says that the gods envy humans "because we're mortal—because any moment might be our last."
In Vamps, this is one reason Goody and Stacy decide to give up vampirism and become human again. The other reason is that Stacy's unborn child won't survive unless Stacy becomes human. Goody and Stacy had fun as vampires, but admit that "being young is getting kinda old". Goody dies as a result.
W-Z
We Are the Night: Charlotte is depressed with being immortal, because she had a husband and daughter who were left behind when Louise made her a vampire. After watching her now very old daughter die in a nursing home, Charlotte takes her own life.
The angelic protagonist of Wings of Desire (and its American remake, City of Angels) gives up immortality for love as well.
Exploited in The Wolverine by Ichirō Yashida to convince Logan to accept his "gift" of growing old and dying so he can live beyond his natural life span.
The cult film Zardoz features a future Earth which has degenerated into two classes — the "Brutals", a race of mortal slaves, and the immortal "Eternals." who live lives of purposeless luxury. Occasionally, an Eternal will develop a mental illness which makes them fall into a state of catatonia. (These people are called "The Apathetics"). If an Eternal commits a crime, they can be punished by being artificially aged (although they don't die — they just become permanently decrepit). The end of the movie has most of the Eternals joyously welcoming their own destruction at the hands of the "Exterminators," a primitive warrior class to whom the main character belongs.
