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Negligible senescence largely fits the bill.
Negligible senescence is a term coined by biogerontologist Caleb Finch to denote organisms that do not exhibit evidence of senescence (biological aging), such as measurable reductions in their reproductive capability, measurable functional decline, or rising death rates with age.
Biological immortality is the ...
36
"ageless" would work as it means: something (or someone) that does not look or appear to grow older
Elrond's face is described as ageless (lotr, many meetings)
35
This could be the 2007 movie The Man from Earth:
The plot focuses on John Oldman, a departing university professor who claims to be a Cro-Magnon (or Magdalenian caveman) who has somehow survived for more than 14,000 years. The entire movie is set in and around Oldman's house during his farewell party, and the plot advances through intellectual arguments ...
35
(OK, let's not work ourselves into a place where everything is like everything else.)
Although TVTropes provides some examples of sucky immortality from ancient mythology, these are really just examples for a few unfortunate individuals, as a special punishment of the gods. Other mortals were made immortal and it was awesome for them.
But the idea of of ...
33
The story is "The Last Answer" by Isaac Asimov.
First published in the January 1980 issue of Analog Science Fiction and Fact, also contained in the collections The Winds of Change and Other Stories (1983), The Best Science Fiction of Isaac Asimov (1986) and Robot Dreams (1986).
After Matemáticos Chibchas correctly identified the author, I was able to find ...
26
Hercules, a.k.a. Heracles, hit his master Chiron the centaur with a poisoned arrow as friendly fire during a battle. Chiron was immortal in the sense that he would never age and would live forever, and also immortal in the sense that he wouldn't die from the poison. Dude was the best healer ever, but he wasn't able to heal himself and the pain was unbearable....
24
This could be the book Crossing The Line.
The main character in the series is Shan Frankland. She is infected with an alien parasite/symbiote called the C'naatat that confers immortality. In chapter 22 of the book she voluntarily exits the airlock rather than face capture.
23
Undying is a term that refers specifically to a state of never being in a process of dying (such as Tolkien's Undying Lands), and applies mainly to life, rather than ideas, art, or appearance. It does not necessarily mean being immune to being killed or destroyed, but rather to not being subject to life's usual condition of growing progressively closer to ...
22
I'm pretty sure that's Mayflower II by Stephen Baxter, published separately as a chapbook but also collected in Resplendent. It has all of the elements that you mention, except that there are five ships rather than three and the protagonist's voyage lasts 25,000 years rather than 10,000.
The story begins on Pluto in the distant future. Its inhabitants,
...
22
Sounds like The Taste of the Dish and the Savor of the Day by John Brunner.
"I found that something brown and nondescript had been dumped on my plate..."
"I had only taken a small forkful; nevertheless, as I rolled it across my tongue, choirs and and flowers burst into bloom and new stars shown in the heavens."
It goes on to describe how ...
21
A while back I read a science-fiction short story that I very much want to re-find.
"Backfire" by Ross Rocklynne.
I probably read the story in a "Best of the Year" anthology or a "Best of 'If'" type collection or the like.
You must have read it in Groff Conklin's Omnibus of Science Fiction.
The story has got to be at least 10, 15 years old but likely way ...
21
I believe this is "A World Out of Time" by Larry Niven.
From the Wikipedia description:
The Earth's climate has changed, despite its new location in orbit around Jupiter. Among the most important changes is the increased surface temperature; the poles are temperate, while the former temperate zones reach temperatures of over 50 degrees Celsius (...
20
The Live-Forever Machine
This is an early work by Kenneth Oppel, the author of such well-known works as Airborn. It’s got "machine" in the title, of course.
According to the Goodreads description:
Alexander, guardian of the secret of immortality, only wants to
preserve the past. His nemesis, Coil, will do anything to destroy it.
Within the eerie ...
17
This is almost certainly Alfred Bester's The Computer Connection (aka Extro) which has many points of similarity with your list: group of immortals, Native American bride, power struggle, etc). Flipping through the book, I found the cancer reference too, although it's some kind of awful leprosy/cancer combination called Lepcer. It can strike the immortals ...
17
Turning to roleplaying games, GURPS uses "Unkillable" for "immune to death by violence" and "Unaging" for "never growing older once mature".
16
I believe this is Ben Bova's series, Orion, about an immortal cave man, following his defense of Humanity through the ages. There are six books in the series.
John O'Ryan is not a god...not exactly. He is an eternal warrior destined to combat the Dark Lord through all time for dominion of the Earth. Follow him, servant of a great race, as he battles his ...
15
Eternal youth. From Wikipedia:
Eternal youth is the concept of human physical immortality free of ageing. The youth referred to is usually meant to be in contrast to the depredations of aging, rather than a specific age of the human lifespan. Achieving eternal youth so far remains beyond the capabilities of scientific technology. However, much research is ...
15
@duskwuff gives one small example of the ancient Greeks discovering problems with immortality. However this is a relatively minor point in one fable.
More significantly, the ancient Greeks invented the concept of an afterlife for sinners as a place of eternal suffering, a concept most notably picked up by Christianity and called Hell. The Greeks called it ...
14
The story is Hardshell by Dean R. Koontz, previously identified as the answer to Short story: Cop chasing serial killer, both are shape shifting aliens. I read it in Koontz's anthology Strange Highways.
The story is exactly as you describe. The scene where the protagonist (Frank) kills the serial killer (Skagg) is:
The inescapable embrace with which Frank ...
13
It seems to me that other answers describe intentional eternal suffering inflicted by gods instead of the immortality being itself the cause of boredom or unhappiness as asked in the original question. Still, as @duskwuff said, the trope is prehistoric. For the closest and earliest example I can think of, we need to look no further than at the earliest ...
12
Stars, Won't You Hide Me? by Ben Bova
Mankind invents immortality but the raw ingredients come from the Flower People. For each human made immortal a flower person must die,
The Others decreed that mankind must become extinct for this crime. Especially since man did this once before. Then the Others were merciful and only blew man back into the stone age....
11
I am 56 and read (as a teen in the 70's) a short story
"Perchance to Dream", a short story by Sally A. Sellers, previously identified as the answer to the question Identify this story about a quickly healing woman; first published in Isaac Asimov's Science Fiction Magazine, Spring 1977, available at the Internet Archive. Does any of these covers look ...
11
Though you have indicated this is a short story I believe this may be the Robin Cook 2000 novel Abduction.
Points that match:
I read this short story probably 5 to 10 years ago.
Partial check. The novel came out in 2000.
There is this utopian land where the people are basically immortal thanks to being able to transfer into a new body when they ...
11
"To Be Continued", a short story by Robert Silverberg, first published in Astounding Science Fiction, May 1956, available at the Internet Archive. Maybe one of these covers will ring a bell.
Plot summary from Majipoor.com:
This story presents a version of extreme longevity that's a bit different than most (Heinlein's Lazarus Long and so on). Gaius Titus ...
10
My mind keeps circling back to Keith Laumer, but I know it's not The House in November... Could it be The Long Twilight (1969) by Keith Laumer?
For hundreds of years, Grayle and Falconer have battled across Earth. Their conflict has created myth (Falconer is also knows as Loki, Grayle as Thor) but has been largely personal until now. With the perfecting of ...
10
I believe that's "The Days of Solomon Gursky" by Ian McDonald (the two anthologies it's been in that are over a decade old are The Year's Best Science Fiction: Sixteenth Annual Collection and The Furthest Horizon: SF Adventures to the Far Future, perhaps you read it in one of those). You can read the first couple pages on google books here, you can see it ...
10
It is possible that you are looking for In the Face of My Enemy by Joseph Delaney, published in 1985.
Eighteen thousand years ago a priest ascended a high place, there to hold converse with his gods. That night the gods chose to bless him with their physical reality. Alas, mortal flesh cannot bear the presence of godhead, and so he died.
And was reborn. But ...
10
Pretty sure this is Ajin: Demi-Human, which originally aired in 2016.
The synopsis roughly corresponds to the general premise you described:
Mysterious immortal humans known as "Ajin" first appeared 17 years ago in Africa. Upon their discovery, they were labeled as a threat to mankind, as they might use their powers for evil and were incapable of ...
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