A huge part of Coach Munakata's character and motivations in Aim for the Ace! are centered on how he has three years to live due to leukemia.
This is parodied with "Coach" Ohta of GunBuster, who is poisoned by space radiation and is presumed to only have six months to live. This sends Kazumi into a Heroic BSoD when she thinks he's passed on while she and Noriko are preparing to fight the Space Monsters in the titular mecha. Not only is he still alive when they get back, Kazumi and Coach get married and spend a year together before he finally does pass on.
Attack on Titan: Chapter 88 reveals that Titan Shifters are all subject to what is referred to as "The Curse of Ymir", which gives them thirteen years to live before their body hits its limit and starts breaking down. It's claimed that Ymir Fritz, the being who originally held the powers of the titans, died thirteen years to the day after gaining her powers. This doesn't bode well for Eren and Armin as by best count the former has eight years left, probably even less, while the latter only just gained powers before discovering this.
The events after the Time Skip focus heavily on this particular plot point. Marley refers to it as a "Tenure", and begins the process of selecting the next Warrior in the final years. Gabi, Falco, Udo, and Zofia are all candidates being considered to inherit the Armored Titan from Reiner (who has 2 years left), while Colt has been selected to inherit the Beast Titan from Zeke in a year's time.
After Zeke betrays Marley and is on Paradis Island, it's revealed that the person who will inherit the Beast Titan is actually Historia Reiss, as she's the only other surviving character with royal blood. Historia is currently pregnant, and her child is expected to inherit the Beast Titan after Historia's term is over. It's discussed that Historia was made pregnant so that they'd have to keep Zeke alive for as long as possible, as Historia's baby would die should she be transformed while pregnant, although exactly who's responsible isn't yet known.
Motorball champion Jashugan in Battle Angel Alita. The modifications that make him the elite athlete/fighter that he is are killing him, but he'd rather go down defending his title than retiring.
Bokurano. The cast soon learns that this is true for the whole lot of them as Zearth's pilots; a lottery picks out who'll be next, and the time is decided randomly. The main story is arguably to see how each of the characters deal with this knowledge, in light of their own lives.
In Boku no Hatsukoi wo Kimi ni Sasagu, main character Takuma is expected not to reach adulthood. He may die before he becomes twenty due to a heart disease he was born with.
In Buso Renkin, when Kazuki becomes a victor he has six weeks before the change becomes permanent. He vows to kill himself before his Superpowered Evil Side becomes permanent.
At the end of Ceres, Celestial Legend, it's revealed that Tooya has only a year or two left to live. Both Tooya and Aya know it, hence the scene where Tooya begs Yuuhi to take care of Aya and their baby when he kicks the bucket. Though he did add that he's not sure.
In Chrono Crusade, Rosette made a contract with Chrono, a demon, saying that she will give him the ability to use his powers at the cost of her own lifespan. The sign of their contract is a watch Rosette wears around her neck, which counts down the time she has left to the very minute.
Also, it's revealed in flashbacks that Mary Magdalene had seen visions from her childhood that she would be killed by someone named Chrono. Once she meets him, she's well aware that it means she will soon die by his hand, but willingly leaves with him anyway, believing that You Can't Fight Fate.
The only power of Oruha in Clover is to know the exact moment she will die. And the readers know too if they started reading the volumes in order.
In Death Note each human has an "expiration date" that Shinigami, and humans who've traded half their remaining life for "shinigami eyes", can see.note When Ryuk demonstrates this by looking at Light, his lifespan is depicted in a series of numbers that have to be converted into "human time", he refuses to tell Light (and the audience) the result to avoid ruining the fun.Death Notes cause those whose names are written in them to die sometime before their original appointed time, and when a shinigami does that their victim's remaining time is added to their own, humans aren't so lucky. The only exception where humans can gain time is if a Shinigami breaks the rules and uses their Death Note to save a human's life such as Gelus, who had a crush on Misa and knew that her "expiration date" was short since she was going to be killed by a stalker. Gelus proceeded to use his Death Note to kill said stalker, and he himself dies shortly after, and Misa inherited whatever time Gelus had left as well as his Death Note much later.
Dinosaur Sanctuary: Dr. Shiranui claims that cloned dinosaurs tend to be far more unhealthy and sickly than natural bred dinosaurs from the Barakan Island population, with almost all of them never getting to live out their full lifespan. One of the cloned dinosaurs, Roy the Dilophosaurus, already suffers from gout and kidney failure despite his young age, so it’s unlikely he’ll be around for much longer.
After the death of Raditz in Dragon Ball Z, the readers/viewers learn that both Kami and Piccolo are aware that they are going to die in the next year when the other two Saiyans arrive. While Kami doesn't know the course of their deaths, he theorizes that this knowledge might have changed Piccolo's personality and status as a demon, which explains why Piccolo trains Gohan and does show him mercy. And indeed, Piccolo dies by sacrificing himself for Gohan, leading to Kami's death.
When Krillin meets Grand Elder Guru, the latter reveals he has only a short amount of time to live. He does die because of his old age, but the progress was accelerated by Freeza's action. When the Grand Elder is revived by the Dragon Balls, he only gains the stolen lifespan back. But that's long enough for him to put his affairs in order, appointing his eldest son Tsuno as the new Grand Elder and ensuring that the Namek Dragon Balls would remain functional.
In recent chapters of the newly revived manga D.N.Angel, Satoshi has told Daisuke that all members of the Hikari family die young, and he believes he's near his own death.
In Fist of the North Star, Rei is hit with an attack by Raoh that would kill him painfully in three days' time. While he's able to rescue Mamiya before his deadline, it seems as though Yuda, a fellow Nanto practitioner who held her captive and whom Rei wished to defeat to avenge her honor, would evade him before he died. Thankfully, Toki was able to give Rei one more day with his medical application of Hokuto Shinken, allowing him to defeat Yuda.
Due to the incredible strain of keeping the family in some sort of order, the heads of the Sohma family in Fruits Basket never live past thirty. That's what, in fact, made Akito's father Akira ill... and ultimately killed him. Akito shows signs of illness in the anime and that's her Freudian Excuse, but in the manga, her bad health seems to come more from deep seated psychological problems, courtesy of her Manipulative Bitchmother; when she gets better, the signs of illness seem to disappear.
Alfons Heiderich from the Fullmetal Alchemist: The Conqueror of Shamballa. He knows he's gonna die soon of cancer due to breathing rocket fumes, and he's desperate to finish his project for the rocket in time.
The 'players' in Future Diary have what is known as a BAD END: When their future-revealing diaries get an entry that reveals when they'll die, death is all but certain to occur at that point. There is a chance to Screw Destiny involved and the main character has managed to do this several times, in no small part due to his Stalker with a Crush's device, which gives fine-detail information about the how as regards to him.
Also, it turns out that the reason for the game is that the god of that world's days are numbered, and the world will end if that happens before he finds a successor. Why that issue needs to be solved with a no holds barred Battle Royale is anyone's guess, but God Is Evil in this series.
Yuno (for reasons unrelated to her health). Her days are numbered because she essentially volunteers to die at the game's end so that Yuki can become a god.
In Gakuen Alice, Natsume Hyuuga suffers from the life-draining Alice whereby he exchanges his life for a limitless Alice. Caring about his friends, he kept his illness a secret from Mikan and Ruka so they wouldn't worry when he uses his powers.
Grave of the Fireflies has a scene in which Seita and Setsuko, the brother and sister who serve as protagonists, capture a large number of fireflies and keep them nearby overnight. The next morning, all the fireflies are dead. Given the number of people who are killed by bombs or starvation in the movie, as well as its connection to the title, this scene is obviously meant to represent something beyond dead insects.
The premise of Ikigami: The Ultimate Limit is that anytime at all, anyone between the age of 18 and 24 might get their "death papers", informing them that they have 24 hours left to live.
In Inuyasha, Miroku's Wind Tunnel is a curse inherited from his father which dooms him to an early death unless the source of the original curse, Naraku, is killed. After an incident in which he absorbs massive amounts of toxic miasma trying to take Naraku out so that Kohaku won't have to be sacrificed, the time frame of Miroku's impending death moves up from "sometime in the nebulous future" to "any day now." When Naraku is defeated, said Wind Tunnel disappears.
In Jujutsu Kaisen this concept is actually worked TOWARDS by Yuji Itadori to reduce that number as much as possible. Although, nobody knows how long it will take, Once he consumes all 20 of Sukuna's fingers he's scheduled to be executed so the demon can be properly exorcised and wipe out their curse before it can exert itself on the world. Yuji has accepted this as his duty and the way he chooses to die.
Chapter 242 of Kaguya-sama: Love Is War revealed that Kaguya's father Gan'an was dying with maybe a few weeks left at best, and they pass away offscreen 26 chapters later. The exact cause is never specified, though the fact that they were in their 80s and had already suffered a stroke several months prior means it can probably be chalked up to old age.
Precia from the first season was suffered from an Incurable Cough of Death and mentioned at one point that she didn't have much time left. Exactly what she was suffering from is never specified in the main series (in the movie continuity, it's the magical equivalent of radiation poisoning). She ended up suffering a Disney Villain Death before it could do her in, though she probably only had a few weeks left otherwise.
Hayate was bound to the Book of Darkness, which was slowly eating away at her life force and had rendered her paraplegic. The plot of A's was set in motion by the Wolkenritter attempting to satiate the book's hunger with stolen Linker Cores in the hope that it would reverse (or at the very least halt) her deteriorating condition. Thanks to her being freed from the book's influence at the end of the season, she ends up making a full recovery and eventually regained use of her legs.
In The Battle of Aces, it's stated that Reinforce Eins doesn't have much time to live in spite of having avoided sacrificing herself. This becomes obvious in Gears of Destiny, where she is Nerfed.
Macross Frontier has this come to Sheryl Nome late in the series, and it's heartbreaking, especially how it ties into Break the CutieandBreak the Haughty. Luckily for her, while Ranka can't get rid of the infection, she manages to move it to a far less lethal place in Sheryl's body and saves her life..
Macross Delta repeats a similar plot point with Freyja, whose overuse of her Rune has caused her lifespan to decrease massively, with the final two episodes of the series focusing on her showing signs of her species' old age. In Absolute Live, unlike Sheryl, it eventually kills Freyja.
In Magic Knight Rayearth, Eagle Vision is Secretly Dying thanks to his overuse of his country's mentally-powered technology. (The versions differ slightly in that he will become comatose rather than dead in the manga, but it's still effectively the end of his life.) Although he keeps it from his friends, Eagle is well aware that he doesn't have much time left and takes it as license to be utterly reckless and ruthless in his quest to become Cephiro's new Pillar.
The conceit of Mahoromatic, where the protagonist is a gynoid with limited battery life remaining. Each segment of the anime and manga ends with how many days she has left to live.
In Mobile Fighter G Gundam, the siblings from Neo Mexico Gina and Chico Rodriguez already know that Delicate and Sickly Gina's Soap Opera Disease is incurable and that she's almost done with her life. Chico becomes the Neo-Mexican fighter not to get a miracle cure, but to bring her to Earth and give her a chance to die peacefully. Thanks to Domon and Rain, they get it.
My Daemon: It’s established in the first episode that Kento’s mark on his face actually contains a Daemon particle, and if said particle hatches into a Daemon, Kento would die in the process. Indeed, the doctor tells Kento's mom that the possibility that Kento would reach adulthood is rather slim.
Yoite in Nabari no Ou uses a dangerous jutsu called Kira which essentially kills his targets using his own life force as bullets. As a result, he's dying by inches throughout the series, since every time he uses his power he loses a bit of his life that he can't get back. This is a source of non-stop anguish.
A later revealed part of the backstory of Gold Roger is that he had contracted an incurable terminal illness that gave him a limited time remaining to live. Being a badass, he decided that, if he was going to die anyway, he might as well conquer the Grand Line first. He does, making him the only person thus far to manage it. It's also the reason the Marines were able to capture and subsequently execute him, as Roger turned himself in as part of a Thanatos Gambit.
It was revealed that Trafalgar Law did not have much longer to live when he asked to join the Donquixote pirates as a child. The only reason he's managed to survive to the current timeline was because of the actions of Doflamingo's kindhearted brother Rocinante/Corazon.
Another disease would claim a character. During Bartholomew Kuma's backstory, his friend he knew since they were slaves name Ginny would later contract a disease that's even rarer than Law's White Amber Lead: Sapphire Scales. This disease causes sapphire-like stones to form on someone which will eventually kill them. Naturally, Sapphire Scales also is incurable at the time due to how rare it is and with Ginny being forced to become a wife to a World Noble, Ginny was screwed until the disease finally claimed her life (not before sending a farewell letter to Kuma whom she truly loved). Kuma would then take Ginny daughter, Bonney, as his own daughter to raise in her place. However, Bonney herself would later would soon contract the Sapphire Scales disease passed from her mother leaving a worried Kuma to search frantically for a cure. In the meantime, he also tries to not worry Bonney by saying her scales make her special and even gives her the full name of "Jewelry Bonney." Though still worried that this disease will claim her life like it did with Ginny, Kuma was eventually able to enlist the help of Dr. Vegapunk who agreed to help cure Bonney of the disease in exchange for Kuma helping him with his latest project.
Xerxes Break in PandoraHearts. His body is slowly breaking down from the strain of being Mad Hatter's contractor. Mostly because it's the second time he's been a contractor. The first time was an illegal contract.
In Plastic Memories, Giftia can only be active for 81920 hours (about 9 years). According to the SAI Corporation, they lose their personalities and memories when they reach their expiration date, effectively "killing" whatever personality the android had up to that point.
Ashitaka spends most of Princess Mononoke with a curse on his arm that is slowly spreading until it will kill him. When the Forest Spirit gets its head back, Ashitaka, San, and the villagers with leprosy are cured.
The Reveal of Puella Magi Madoka Magica, that being that the Soul Gems borne by each Magical Girl are darkening over time due to use of their magic and negative emotions like sadness and despair. Though cleansing Soul Gems is possible through the use of the Grief Seeds left by the monsters that they kill, it is only a matter of time before the Gem darkens completely, turning into a Grief Seed and turning the Magical Girl into one of the very monsters that she and the others fight. No Magical Girl can escape this fate, and there's no way to change the rule, well, except one. In the new world written by God Madoka, this is softened. The Soul Gems are still prone to overuse and darkness, but the girl who falls victim to it will Ascend to a Higher Plane of Existence instead.
Purple Eyes in the Dark reveals that humans with the ability to turn into an animal form tend to not live very long. Rinko's mother died early on, said to be because she carried the gene with this ability.
Rain's Head: The titular character is revealed to have suffered from a terminal illness, which gives her only three years to live before her head would be "shrunk" by Claroa.
Ranma ½: Due to a serious injury Shinnosuke suffered years ago, he needs Water of Life, which his grandfather, his only human companion for much (if not all) of his life, gathers and provides for him to stay alive since his grandfather knows of his condition while he's himself oblivious to it. Unfortunately, the healing effect of the Water of Life on Shinnosuke grows less and less potent as time goes by, requiring him to take more and more of it in increasingly shorter periods. Worse, the springs from which the Water issues have been drying up. His grandfather realizes that — one way or another — Shinnosuke is doomed to die. Near the end of his story arc, however, his grandfather applies the source of the Water of Life on the scarred area of Shinnosuke's body, which permanently heals him.
It's implied that Kurumi from School-Live! won't survive to the end of the series. Her health is quickly deteriorating because the vaccine used to stop her from becoming a zombie doesn't work forever. At the very least, she believes she is dying and has told her friends to prepare for that.
With Power Degeneration being rampant in Snow White and Seven Dwarfs, various characters are dying for different reasons and have all gracefully accepted their inevitable deaths. By the end, Ken, at least, has a temporary cure as long as the doctor who can provide it remains alive, but despite a few hints of hope, there's no way to save the the Ushio brothers.
Golems in Somali and the Forest Spirit live for exactly 1,000 years, at which point they stop working completely and become one with nature. At the start of the story, Somali's "father" has less than two years of life remaining, compelling him to return her to her birth parents before he passes.
In Tokyo Ghoul, the flawed Half-Human Hybrids known as "Half-humans" have a shortened lifespan compared to either parent race. While their external bodies remain youthful in appearance, their bodies begin to break down as they reach their mid-20s. The eldest known Half-human, Kishou Arima, was in his early 30s when he chose suicide over a slow death from old age.
Thors is essentially doomed the moment Floki and the Jomsvikings track him down to Iceland and knows it. He intentionally cuts down on the crew he takes with him 'to war' to limit any collateral damage in an assassination attempt, and spends his last days trying to impart wisdom to his son and arranging for his family. When the assassins finally come for him, he commits a Heroic Sacrifice to save his travelling companions from his own fate knowing he's not escaping alive either way.
Bjorn takes a gut wound from a sword. In a setting without antibiotics, this essentially means a slow death from an infected wound and he's aware of it, which is why he chooses death in a duel.
A cicada youkai in Yo-kai Watch believes he only has a week to live and tries to extend his life. After finding out it's a moot point he tries to make the best of what little time he has left... However, being a yo-kai he is already dead and he just passes out exhausted after his timer is up, because he spent so much time trying to have fun and didn't sleep much.
Kouse's mother Saki realized she didn't have much time left in her life due to her illness. Because of that, she taught Kousei as much as she could about how to play piano accurately according to the music score, giving him the nickname "Human Metronome". She did this with the hope that Kousei would be able to make an income and have a decent life with his piano playing after she was dead. Her plan backfires horribly after Kousei gets fed up with her abuse and harsh critique. She died shortly afterwards, leaving Kousei dealing with trauma that made him unable to hear his own piano playing at the start of the series.
After she saw her parents crying in the hospital waiting room one night, Kaori realized she didn't have much time left in her life, so she decided to live a full and happy life before passing away. Then, she told the titular lie about liking Watari, for the sake of approaching Kousei, the guy that become her reason to become violinist and also to help Kousei overcome his trauma so that he could return to the music world once again and continue his journey as a musician.
