It also directly addresses the incest issue - namely, the Adam finds his Eve so annoying he plans to leave her for their first daughter. On the other hand, the story never precludes the possibility that more successful Adam And Eve Plots happened.
Played in Animorphs, the book "The Change." There are several Adam and Eve references to Jara Hamee and Ket Halpak, the first two free Hork-Bajir since the Yeerks enslaved them.
Subverted in "The Silent Towns". A man wakes up to find that he's been left on Mars by accident after most of the Martian colony has gone back to Earth. He begins dialing phone numbers in a desperate attempt for human contact and manages get in touch with a woman, who he begins to fall in love with (based on their brief phone conversation). When they finally meet, he finds her obnoxious and decides he'd prefer a life of isolation.
The final story plays the trope fairly straight though, although it leaves it open whether or not "Adam and Eve" will actually meet up (and the human race will continue).
In Orson Scott Card's Homecoming Saga, sixteen people (only four of whom had no genetic connection to someone else in the group) from the planet Harmony were selected to return to Earth and re-establish the human population. It was established that since the Oversoul (the supercomputer that had been running the planet for millennia) had been running a breeding program for just this situation, any recessive traits that would pop up in such a closed population had been bred out of them (it was also revealed that Harmony was not the only such human-populated planet, nor was it the first to return to Earth).
There was a "short short story" that started to set up this trope in the style of the Twilight Zone episode mentioned below... then Adam was accidentally castrated.
Subverted in a completely different way by Larry Niven's short story "What Can You Say About Chocolate Coated Manhole Covers?" The story begins with the main characters at a party having a fun conversation. They speculate on how the Adam and Eve legend could work in real life, purely as an intellectual exercise. They conclude, for the obvious reasons, that one pair could not populate an entire planet. They come up with an elaborate scheme based on Real Life stock breeding techniques, involving many pairs and small groups that are isolated from each other by geography. Then... an alien kidnaps the protagonists, strands them on a planet orbiting Alpha Centauri, and tells them that they've just figured out the aliens' secret plan for breeding an 'improved' form of human being.
Parodied in a Harlan Ellison short-short story, "The Voice in the Garden" where two humans who are sole survivors of some sort meet each other and decide to do this. The woman is of course named Eve, and the man... George.
In one of Michael Swanwick's "element" short-shorts, an experiment creates a new universe populated by one man and one woman. The man's name is Adam, so naturally the woman takes a new name... Jennifer.
In Meredith Ann Pierce's The Firebringer Trilogy, four hundred years before the books begin, the unicorns' princess and warleader sends four scouts out to seek verification of claims being made by wyverns who want to emigrate to the same territory as the unicorns. Quite some time after the scouts leave, one comes stumbling back with the news the four were sent to get, and notes that one of their companions died along the way. The other two were kept as hostages. Fast-forward four hundred years to the travels of Jan, the books' main character, and when he reaches that part of the world what does he find but a small, well-protected herd of unicorns who all look very much like the descendants of the last two scouts. And yes, the incest factor is acknowledged. There's also the implication that these unicorns wouldn't have survived to breed to these numbers if they hadn't had the protection of powerful dragons.
Xanth has numerous examples of this trope with novel types of crossbreeds. Typically, it starts with one crossbreed looking for another of his/her kind to mate with. Somehow, he/she finds one, and then a few books later their child goes on a similar quest.
Toyed with the the first novel. After doing research in Castle Roogna, Trent is the first person to realize that even though there are plenty of humans around, without fresh blood the omnipresence of magic will eventually lead to humanity's extinction. They will keep producing more crossbreeds, or just plain mutate from too much magic (Humphrey is implied to be on his way to becoming this). As inconvenient as the sporadic invasions from Mundania are, they provide fresh, non-magical genetic stock for humanity.
Eventually subverted in the case of the winged centaurs. When we first meet them, there's just the two of them and this trope seems to be in full force. In later volumes, we find out that they've been gathering volunteers from other races to be transformed by Magician Trent into winged centaurs.
Averted in "Rescue Run", one of Anne McCaffrey's short stories, by the handful of colonists left alive on the Southern Continent of Pern. Convinced that all other humans have been wiped out by Threadfall, domineering jerkass Kimmer forces marriage on the sole remaining female in his group, then refuses to allow any further breeding due to the limited gene pool.
In The Magician's Nephew, Aslan appoints a London cabby and his wife to be Narnia's first king and queen, as well as its first (and only) human inhabitants. Incest issues are averted when their kids grow up to marry wood nymphs and other spirits. This eventually dilutes their bloodline to a point where, when the White Witch returns to conquer Narnia, there's apparently no one left in Narnia who's human enough to contest her claim. After a time, Aslan sends the Pevensie children to do so.
However, Narnia has a sister country in their ally of Archenland, which was fully populated by humans. Also, the subornate island nations, and the southern enemy nation of Calormene. There's not much explanation for how these people got there, though it might have been similar to how the Telmarenes showed up. C. S. Lewis didn't expect to write more than the first book, until popular demand had him go back and expand the world.
According to CS Lewis' official timeline for the history of Narnia, the first humans - as well as intermarrying with Narnian nymphs and dryads and stars and the like - also quickly spread out within a handful of generations to colonise the until-then mostly barren neighbouring lands of Archenland and Calormene. All the part-humans in those three lands could trace their heritage back to the very first humans to enter Narnia (Frank and his wife). The Telmarines, by contrast, were pirates shipwrecked on an island who accidentally crossed over to a land bordering Narnia, established themselves there as the Kingdom of Telmar, and invaded Narnia shortly after the Pevensies left at the end of The Lion, the Witch, and the Wardrobe.
Another classic subversion is "Adam and No Eve" by Alfred Bester, in which the protagonist would be happy to fulfill the plot, but no woman is available. At the end of the story he drowns himself so that his bacteria will survive in the ocean and hopefully evolve into a new sentient species one day—needing no Adam and no Eve.
Stephen Baxter's The Time Ships: an expedition from an alternative Great Britain becomes stranded in the deep past after an attack from a time-traveling bomber from their enemies in their own time. They survive, and the protagonist gets to watch them rise from a tiny tribe to a space-traveling civilization as he travels in time, a sequence which is rather unpleasantly like watching mold conquer a petri dish.
Z for Zachariah: Anne imagines this with Mr. Loomis since they are, or so she believes, the last survivors in America and possibly the whole world following a nuclear war. Turns out he was way ahead of her, leading to Attempted Rape and causing her to run away from him, which forms the catalyst for the ending of the book.
Olaf Stapledon's future history novel Last and First Men has at one point the entire mankind reduced to roughly a dozen individuals. They manage to repopulate the Earth with apparently no catastrophic effects from inbreeding. (Then again, the end result is a whole new species of humanity, albeit a better species in many ways.)
C. S. Lewis' Perelandra: It's another planet's version of Adam and Eve, but they still live in paradise and a world without sin or suffering.
A mild case occurs in Mikhail Akhmanov's Arrivals from the Dark series, where an alien race purchases a pair of eagles for their collection and releases them to roam on one of their preserve worlds (they live in orbital habitats). A century later, the eagles number in the hundreds and have adapted to the new world. This happens again, when another pair of eagles are taken from this world to a remote human colony on a world with a much harsher, colder climate. Despite this, the eagles once again increase their numbers and thrive.
Andrey Livadny's novel Ark is set aboard a Moon-sized (literally; it's actually the hollowed-out Moon with engines attached) Generation Ship sent a long time ago from Earth to find and collect alien life and put them in specially-adapted habitats. A catastrophe kills the command crew and forces the rest of the humans to live in one of the habitats, leaving the ship's AI to fly the damaged craft. Over time, the humans regress to near-Medieval state and forget their origins. At the end of the novel, the Ark crash-lands into the sea on a habitable world orbiting a yellow dwarf, and the first person out is an old shepherd named Noah. How the ship ended up in the past is not explained. It is also not clear what happened to the aliens on-board.
The post-apocalyptic story "Mecanoscrit" by Manuel de Pedrolo ends with the creepy variant that the Adam-character dies, and the Eve-character wondering if she would live long enough to have her infant son grow up and have children with him, and a footnote stating that the entire story is a historical document.
Keep in mind though that the entire story is written from Alba's ("Eve") perspective, save for the last episode, which is stated to be an analysis from a future investigator, who wonders about its authenticity but pretty much states that if what's on the text is true, then Alba is the mother of modern mankind.
With all the religious symbolism that shows up in Greg Egan's Permutation City, it's only fitting that it should end with Paul and Maria setting off together into their own newly-created universe.
In His Dark Materials Lyra and Will end up being this at the end to ensure that Dust continues to flow down and into the worlds. Phillip Pullman even goes further with it and creates a serpent out of Mary Malone and a garden of Eden type world. In this case, what was important was not the mating and reproduction (they didn't produce a child a together from their one time), but the act of intimately connecting to another sentient being and sharing/expressing the love they felt.
In Bob Shaw's short story Call Me Dumbo, a family live in an isolated cottage, but it turns out that the parents were the sole survivors of a spaceship crash, and the mother was originally a man on whom the father performed a non-consensual sex change operation and suppressed his/her memory using drugs.
The ending of Invitation To The Game has the characters conclude that the eponymous Game's purpose is to train them as colonists for a new planet. However, they're True Companions with no romantic interest in each other... then they find another group, and realize several such groups have been placed on the new planet, close enough to form relatively accessible settlements, so there will be plenty of breeding material.
In Poul Anderson's After Doomsday, the women are well aware of the flaws of this reasoning; though they know that many people have survived, they are also aware that the men outnumber the women and make plans for polyandry so that every surviving woman will have children by several men.
The Gene Wolfe short story "Procreation" has a variant, and indeed a Shaggy God Story: the writer creates a miniature Universe. Deciding to let the creatures within know how they came to be, he and his sister ('Sis') write an account of the creation and drop it into the Universe. They don't know what to call the book, so just write their names on the cover. 'Gene' + 'Sis'
"Born of the Sun" is a 1934 short story that is probably the reason why most editors had a policy of rejecting stories with this twist on sight. It starts out fine enough, with the heroes managing to build a spaceship to escape the Earth before it is destroyed, and they originally plan to defy this trope by saving as many people as they can. Unfortunately, it seems like the writer thought that he had no choice but to use the trope for this kind of story, because in the last few pages, the villain manages to whip up everybody except the male and female leads into a religious fervor and destroy the original spaceship, even though most of these people were volunteers who showed no sign of believing in the villain's cult at any earlier point in the story. Fortunately, the male and female lead have a smaller spaceship which they use to leave the Earth, but they are all alone. The implication is that their descendants will populate the universe, but then it runs into Fridge Logic that they wouldn't have enough genetic diversity to keep the species going, which the author seems at least vaguely aware of because of the aforementioned spoiler.
During the end of Sea of the Patchwork Cats, with Jen digested and Kara killed by the Queen of Cats, Conrad and Jaji are now the last human on the planet (if Jaji even counts), the ending having Jaji pregnant while Conrad contemplates the future.
The ending of The Maze Runner trilogy. Out of the entire human race, only a select few are able to resist the influence of the Flare virus. They are thus humanity's last hope to rebuild the Earth. However, that last few actually number several hundreds, which is far more realistic than the usual application of this trope.
Richard Wilson's 1969 novelette "Mother to the World" is non-twist variation on the plot. A man and woman wake up one morning to find that everyone else in the world is gone. To complicate matters the woman is mentally disabled. The story revolves around their relationship and won the 1969 Nebula Award for Best Novelette.