There is a subgenre of Speculative Fiction referred to as Dying Earth, named after the Jack Vance series, Dying Earth. Often, these works have a sword and sorcery feel, but with clear hints that this is the future.
To clarify, The Dying Earth is set millions, if not billions, of years in the future, where the Sun is dying and civilization has risen and fallen countless times, and now science has been forgotten and magic has re-emerged.
1984 is set sometime after an unspecified cataclysm (hinted to be nuclear war) caused the collapse of the democratic governments and prepared the way for the rise of the three world powers. Much of the story's creepiness derives from the fact that we can't be sure if anything the Party says is correct, or even if the other enemy states exist at all.
Aftertime and its two sequels are set after a worldwide disaster.
Jonathan Lethem's Amnesia Moon is set in a surreal post-apocalyptic world, after the US has been hit by nuclear bombs. The work is an homage to Philip K. Dick, and reality itself seems to have become a bit unglued by the disaster.
Patrick Tilley's The Amtrak Wars takes place about a thousand years after a nuclear war and revolves around the conflict between the surface dwelling Mutes and the underground based Amtrak Federation.
Neal Stephenson's Anathem has its calendar set the year 0 as the "Terrible Events," a near-extinction level nuclear/nanotechnological war. A rough translation to Earth years puts this in the later half of the 21st century. The main events of the novel are set more than 3500 years from this event. During this time, the planet has gone through at least three other civilization-reducing periods. The main characters' society has even categorized the kinds of post-apocalyptic civilizations that pop up afterwards. During the story's events, civilization has returned to a level similar to the 21st century again, save some holdouts.
Breed to Come is set in a post-human world in which the disease that wiped out the humans led to the rise of several other intelligent species, among them the protagonist's. His eldest surviving relative has spent his life studying the remains of human civilization and acquiring any technological advances that might benefit his people.
The short story "The Gifts of Asti" opens just as Memphir, the protagonist's homeland, is falling to a barbarian invasion. She - the last priestess of a mostly-forsaken religion - follows a standing order about what to do After the End (which was mentioned in prophecy), and takes a prepared escape route. She ends up on the far side of a mountain range to find a vast plain that was glassed in a now-forgotten war.
Sea Siege opens on a small Caribbean island that is having trouble with mutant sea creatures - just before World War III.
Star Man's Son (a.k.a. Daybreak - 2250 A.D.) opens generations after World War III. The protagonist is suffering from his culture's prejudice against mutants.
Angel Notes, set in the Nasuverse, starts years after Gaia (Earth) has died, but both actual Humans and two modified human races lives in the theoretically uninhabitable hell caused by Gaia's dead (normal Humans have to use special suits, though). The survivors have to deal with the Aristoteles, sent by the other worlds to kill the survivors as asked by Gaia in her last breaths.
In Angelfall the apocalypse, caused by angels, happened six weeks ago. Humans already have adapted so far as to use old computer to build a latrine wall.
In H. Beam Piper's short story "The Answer", the protagonists - an American and a Russian - managed to survive the destruction of their respective nations, and are now working in South America. The titular answer is to the question, why was Auburn, New York, the first casualty of World War III - particularly since the Soviets then threw away the advantage of a first strike and didn't follow it up? The town wasn't destroyed by the Soviets, but by a Colony Drop - specifically, of an antimatter meteor - and nobody recognized it for what it was until after one of the protagonists, who witnessed the destruction of Auburn and investigated it, witnessed the results of a similar, artificial antimatter experiment in South America.
Ayn Rand's Anthem takes place after collectivisation has destroyed civilization and reduced the city that is the book's setting to a medieval level. Some of Rand's critics posit that even though it was written before Atlas Shrugged it's a sequel and that the abandoned house the hero finds is all that remains of Galt's Gulch.
Taken Up to Eleven in As the Curtain Falls, where humanity has developed advanced technology, built a spacefaring empire, and been knocked back to the Stone Age three times. The book is set when the third of those empires is just a legend, the Sun has swollen into a Red Giant, and the remnants of humanity live huddled on the dried up seabeds.
Ashes, ashes, one of Rene Barjavel's novels, takes place in a world where electricity has completely disappeared, causing the end of civilization. Humanity gets better in Future Times Three though, thanks to telekinesis and eusociality.
In Rebecca Ore's Being Alien trilogy, Gwyngs are a sapient bat species, but they are the second generation of intelligent life on their planet. They are aware of the "Old Ones" who "died / killed themselves". They don't know which.
In John Calvin Batchelor's novel The Birth of the People's Republic of Antarctica, a convincingly-portrayed international social breakdown is summed up by one character as "There's been no war. Just a bloody shuffle." It is implied that by the narrator's "present", new global social patterns have developed, without detailing them.
Parts of The Book of Dave by Will Self take place in a flooded out England five hundred years after the titular book is discovered and a religion is founded on it.
In The Books of Ember, human society was destroyed by the Disaster, a combination of "the Four Wars and the Three Plagues". However, the titular city was built underground as a safehold for human culture and survives for 200-odd years after the war ended... and then the lights start going out. By the end of the series, people start rebuilding on the surface and things are looking up.
In Elantris, the magic has gone away, leaving the eponymous city a crumbling ruin inhabited by zombies when it had been a borderline-utopia before. The kingdom it was originally capital of is rapidly crumbling as a result, but the rest of the world is fine (if "being slowly conquered by a theocratic empire" counts as "fine").
In Mistborn, something happened a thousand years ago that turned the world into a barren, ash-choked wasteland ruled by an Evil Overlord. Much of the trilogy involves piecing together what actually caused this and in the end, fixing it.
The Stormlight Archive takes this up to eleven, with the backstory revealing that the world is subjected to a "desolation" every few thousand years, and it is the duty of the mythical Heralds to prepare humanity for, and help humanity survive, those desolations.
By the Waters of Babylon by S. V. Benet. Remarkable because it depicts what feels like a world post-atomic-war, complete with ideas of what would and would not be safe to handle after the end—only it was written in the 1930s.
A Canticle for Leibowitz, by Walter Miller, is an interesting version of this trope. The storyline spans over a thousand years, beginning in a post-nuclear war Dark Age. The second part is set in a second Renaissance, with the re-flourishing of scientific knowledge, and the third and final part is set in the equivalent of the contemporary age. The novel concludes with a second nuclear war. One assumes the cycle is due to start again, though, as human beings are by now capable of interstellar travel and at least some of them get off Earth before the bombs land.
Mikhail Akhmanov and Christopher Gilmore's novel Captain French, or the Quest for Paradise has the titular character describe several human colonies that ended up destroying themselves or suffered some sort of natural calamity. Some of these planets remain empty of human life, while one (which suffered a nuclear holocaust) is noted to have been re-colonized by another colony (who then renamed it in honor of their hard work). The novel itself starts on planet Murphy, which has suffered a comet strike half-a-century before, and the population is now firmly in the hands of a theocracy that preaches that the comet was God's Hammer punishing humans for their sins. Prior to the theocracy taking over, the population of Murphy suffered a brief period of cannibalism and overall chaos.
Arrivals from the Dark and Tevelyan's Mission, Akhmanov's book series taking place in the same 'verse reveals that two of the setting's key Human Alien races' current culture is the direct result of major catastrophes that wiped out former civilizations. The Bino Faata experienced two such catastrophes, before the survivors decided that there would not be a third one and embarked on a campaign of endless conquest meant to prevent it. The Kni'lina also suffered two within a relatively short time frame. A rogue planetoid was captured by their homeworld and turned into a second moon, resulting in massive tides, volcanic eruptions, and earthquakes. To top it off, they were hit by a devastating plague that wiped out much of the population on the mainland. The semblance of civilization only remained on isolated islands, which used genetic engineering to make themselves immune to the disease, resulting in many clans, which are, in fact subspecies. Humans had a mild version of this, when Anti Matter-filled Faata ships blew up in major cities all over the world, resulting in millions dead and much destruction. However, it could have been much worse, and humans emerged a galactic superpower.
Children Of Mother Earth takes place after global warming has more or less destroyed most of the planet. Greenland, though, turned green, and the people there developed a nice, stable government.
Neil Cross's Christendom takes place some time after a massive series of global conflicts during which, among other things, America fragmented, the entire population of Japan was wiped out by a Chinese bioweapon, and crashing nuclear satellites bathed large chunks of the planet in radiation.
The Chrysalids by John Wyndham, who liked this sort of thing, is about a society recovering after a catastrophe, which the hyper-Christian characters call "The Tribulation" and is implied to be a nuclear war/disaster. In the protagonist's community, any living thing showing signs of genetic abnormality is considered a Satanic abomination, including human beings. His having telepathy is therefore something of a concern.
Robert Wingrove's Chung Kuo presents a world-spanning empire built after a devastating war ended the world as we know it.
David Mitchell's Cloud Atlas delivers this in two stages. In "An Orison of Sonmi-451" The skirmishes, apparently a series of limited nuclear exchanges have turned much of Earth's surface to "deadlands". Most of what's left is a corportate dystopia run by Megacorps. By the time of "Sloosha's Crossin' an Ev'rythin' After" some other disaster, presumably another nuclear war, has finished even that off and only a few places, like the Hawaiian Islands remain inhabitable.
Comet Dis'aster is set after a destructive comet hits the Earth.
Conciencia y Voluntad takes action in year 2057, after the collapse of the western civilization for a long, non-nuclear war, economic crisis, and climatic change. But it could be worse.
The short story "The Days of Perky Pat" by Philip Dick plays the trope for laughs. Society is split between the younger, more practical generation that is intent on rebuilding and maintaining a functioning civilization, and the older generation, which devotes all its time to escapism in the form of a mass role-playing game involving dolls.
The Death Gate Cycle takes place after two ends. Originally, the world our world, in fact had an advanced technological civilization that destroyed itself through what appears to have been a nuclear war. Shortly thereafter, the return of magic and appearance of elves, dwarves, and two Witch Species turned the world into a Shannara-esque version of the Standard Fantasy Setting. Then the two Witch Species (the Sartan and the Patryns) went to war using the other races as proxies, culminating in the Sartan, fearing that the Patryns would win, completely destroying the world and rebuilding it as four worlds patterned after the four classical elements, plus a Death World where they stuck the Patryns. Then they vanished. The series picks up a millennium or so after this "Sundering".
The Gold Eagle adventure series Death Lands takes place in a post-WW 3 United States plagued by crazed mutants and power-hungry barons.
A localized version in the Russian Shared UniverseDeath Zone is a semi-sequel to the Stalker series. In Death Zone, a mysterious explosion occurs in Chernobyl and four other areas in Europe and Asia, including major cities like Moscow and Saint Petersburg. After the explosions, the areas are covered by bubble-like gravity Barriers that create mini-Scavenger Worlds in each one. Anomalies can be found all over the Five Zones, usually of the deadly kind. Most machines have been turned into strange bio-mechanical hybrids called mechanoids whose behavior mimics that of ordinary animals. Nanobots can be found everywhere with the risk of being "infected" by them and becoming a zombie-like biomechanical creature called a staltech (or techzombie, according to some authors). Most of the populations of the Zones is either dead, turned into staltechs, or evacuated during the initial post-explosion days. Life outside the Barriers continues just as before (even though two major cities are now in ruins), but life in the Zones is very different. At the center of each Zone is an extradimensional tornado that acts as a gateway between them. The only people who can survive in the Zones are called stalkers.
S.M. Stirling's Dies the Fire series begins with a mysterious "Change" in the laws of physics that abruptly makes all powered machinery (even steam engines) inoperable and explosives inert. (Eventually it's revealed that this was caused by what might be called the Universal Mind attempting to stave off an even worse fate for humanity.) Before long most of humanity dies of starvation and the survivors have to rebuild society on a low-tech basis. "Ethnogenesis", the emergence of new cultures, ensues. One state, founded by SCAdians, is modeled on Medieval Normandy; another, founded by Wiccans or neopagans, consciously imitates a Medieval Scottish clan; etc. Large areas are inhabited only by cannibals who have forgotten about civilized culture entirely. The new states are often at war with each other, using armor, swords and bows.
Dinner at Deviant's Palace is set after a calamity left a number of radioactive holes in southern California (and presumably other places further afield, whence news no longer comes since civilization collapsed). Society has rebuilt in a number of walled cities which use distilled alcohol (a fuel, a disinfectant, and a drink) as Practical Currency.
Divergent is implied to be after a major war. Subverted with Allegiant where its revealed that while there was a war, society is still somewhat intact with the US Government still existing but as a shadow of its former self. Though half the US population is dead, many of the Metro areas are filled with crime and fantastic racism. It's also revealed that Chicago is a closed off experiment, one of a few in the Midwest. Itís also implied that the west coast is either uninhabited or possibly isolated. (Itís not clear as the fringe groups don't go there because the terrain is too rough to traverse).
The Dog Stars is set nine years after a super-flu wiped out almost all of the human population and a mysterious blood virus swept in to waste away many of those who remain. Humanity is limited to small packs of marauders and survivors who pretty much kill anyone they see on sight. The environment has also gone a bit haywire for unknown reasons, with many species dying off and the temperature rising.
Most of the Dragonlance novels and adventure modules are set after the Cataclysm, an event in which a fiery mountain (i.e., meteor) fell on the city of Istar and destroyed it and much of civilization with it.
The story in Dream, Delusion, and Reality is set in post-apocalyptic world during 23rd century after mysterious race of invading creatures ruined the Earth.
David Gemmell's Drenai series, initially straight Heroic Fantasy, has increasing hints as it progresses that it's set after the collapse of a high-tech civilization and that its magic is Magic from Technology.
Earth Abides, by George Stewart, depicts life in California after a pandemic wipes out most of humanity.
Edgar Pangborn's novels Davy and The Company of Glory, together with related short stories in Still I Persist in Wondering and others uncollected, take place in the decades and centuries following the 30 Minute War and the Red Plague, a devastating "limited" nuclear and biological war. As civilization slowly and painfully rebuilds itself in what used to be New England the stories focus on individual struggles, triumphs and tragedies. The rigid, mutant-fearing feudal societies depicted therein seem to owe something to The Chrysalids.
Fred Saberhagen's Empire of the East and its sequels series The Books of Swords and The Books of Lost Swords are set on earth thousands of years after civilization was not destroyed in a nuclear war. Instead, the United States activated a device that actually changed the laws of nature to prevent the destruction of humanity by making nuclear fission so much less likely that the nuclear bombs wouldn't work. The good news is that it worked. The bad news is that changing the laws of nature also caused advanced technology to stop functioning, and caused magic to start working. As a result, civilization collapsed anyway, but it did eventually rebuild, albeit along rather different lines.
The short story "Fields" by Desmond Warzel takes place in Cleveland after the world has been taken over by mutant wheat and most of humanity has vanished.
Francesca Haig's The Fire Sermon takes place four hundred years after a global nuclear war. The ruins of the Before are considered taboo, and off limits to everyone, and society now shuns the technology used in the Before in favour of medieval tech. And the best part? Seers like the protagonist get to relive the Blast in their dreams.
Fitzpatricks War takes place centuries after the Storm Times in the late 21st Century, which trashed all electrical and electronic technology as well as devastated the developed world. The Steam Punk Yukon Confederacy in particular emerged from the ashes of the United States.
In Galaxy of Fear: Army of Terror, most of the galaxy is chugging along just fine, but the heroes crash land on Kiva, which used to support a thriving ecology and a native population, but has basically become like The Road — everything is dead, there isn't so much as a blade of grass anywhere, and the natives have become furious wraiths thanks to some kind of horrific experiment.
Rachelle McCalla's The Girl Who Started The War To End All Wars begins in a domed settlement in Nunavut, Canada, housing some of the last remnants of humanity two hundred years after a nuclear war caused by Franz Ferdinand's efforts to make Austria-Hungary a superpower through the development of atomic weapons.
In The Giver Quartet, while the first book The Giver implies that the world "evolved" for lack of a better term, into Sameness, the second book Gathering Blue shows that the world takes place after a major upheaval known as the The Ruin. Not much detail is given about it, but it is said to been an combination of both man-made and natural disasters.
The Green Gods is set on an Earth where, due to a badly mangled version of the Greenhouse Effect, plants have evolved sentience and enslaved humans, who have regressed to a medieval level.
Sterling Lanier's Hiero Desteen books (Hiero's Journey and The Unforsaken Hiero) are set mainly in what used to be Canada, prior to World War III (now long past). The protagonist's mission in the first book is to rediscover computer technology, because his people are running into information management problems and have enough historical knowledge to realize that computer information retrieval could solve them.
Hothouse by Brian Aldiss. The Sun is going nova, half of Earth is covered by a single Banyan Tree, and the few remaining scattered tribes of humans are dying out.
The Hunger Games, which is set sometime several hundred years after a gigantic, unexplained apocalypse that leaves North America as mostly ash. Hundreds of years later, the nation of Panem is set up after this, but is thrown into a civil war with its Districts, which ends with the destruction of the 13th District. After this event the Capitol sets up the Hunger Games, and the book picks up 74 years later. District 13 is revealed at the end of book 2 to have survived the ass-kicking it received by the Capitol, and the reason it hasn't been destroyed since is because its dedicated industry is nuclear materials, and its own nuclear arsenal allowed them to strike a deal with the Capitol to be left alone.
In the Kate Daniels universe, the world is plagued by magic waves. Most of the human population was destroyed during the first magic flare, when monsters flooded back into the world and magic reduced skyscrapers to rubble. The rest of the humans survive by keeping one hand on their weapons or banding together in tightly knit neighborhoods.
In Olaf Stapleton's Last and First Men, 99% of humanity is wiped out in a huge geological upheaval, with humanity thrown back to the Stone Age and forced to crawl back to dominance over several million years, and evolving into the Second Men, who are then destroyed in a war with aliens and leave behind the Third Men, who evolve into the Fourth Men, who create and are destroyed by the Fifth Men, who then abandon Earth after the Moon comes crashing down and Terraform Venus. Eventually, Venus has to be abandoned when the Sun starts expanding into a Red Giant, and the Ninth Men flee to Neptune. Finally, the Eighteenth (and Last) Men die when the Sun unexpectedly goes Nova.
The Last Ship is last because of a nuclear war that left most of earth uninhabitable.
The Last Survivors series, very few humans, moon out of whack, early winters, seething hot summers, people moving around in packs like animals and stealing from their former neighbours just to live another day.
Much of Lucifer's Hammer takes place after a massive comet destroys most of civilization, with only a few enclaves left.
Maddigan's Fantasia, by Margaret Mahy, is set some time 'after the Great Chaos changed the shape of the world'. The Chaos itself is never described or hinted at, but the entire series is spent trying to ensure that the existing state of things doesn't get any worse — which, according to time-travellers Timon and Eden, it's about to.
The German pulp series Maddrax takes place after a comet hits the Earth, moving the axis of rotation, and causing all sorts of mutations and retardations. Intelligent rats, vampires, primitive people, world conspiracies and more arise out of the ashes.
The French Sci-Fi novel Malevil takes place after a nuclear war on Easter Sunday, 1977. The characters are struggling to survive after the apocalypse but they have a key advantage: the titular Malevil is a stone castle and returns to its original purpose as a fortified stronghold.
The Handmaid's Tale takes place in the Republic of Gilead, a theocratic country heavily implied to be the US in the near future, in which the majority of people have been rendered infertile. However, because of the religious fundamentalist styled patriarchy instated by the regime, it is women who are blamed, the concept that men might be equally infertile tantamount to treason. The handful of remaining fertile women are rounded up and forced to act as broodmares for high-status men, and executed or exiled if they fail to conceive.
Mark S. Geston's first two novels are set in decaying future worlds, some thousands of years after an unspecified catastrophe. In Lords of the Starship a scheme is devised to revitalize the economy of a dying country by using its resources to build a seven-mile long spaceship. Once the ship is built a huge battle is fought over it, then the ship turns on its engines and fries the armies who are fighting over it - and then destroys itself. It has all been a hoax by a Mordor-like country, aimed at depopulating and demilitarizing the rest of the world.Out of the Mouth of the Dragon takes places some centuries later when the world's ecology is in its death throes. A young man sets off to prove himself as a soldier, only to realize that there are no noble causes left to fight for. By the end of the book he seems to be the last man alive, sustained by prosthetic body parts, and as the world slowly dies and the sun goes out he realizes that his prosthetics may keep him alive forever in a dead world.
The novel is written in the third person, which would suggest that he isn't.
Manuel de Pedrolo's Mecanoscrito del segundo origen (Second origin typescript) deals with two young survivors of an alien attack on earth trying to repopulate it and preserve human culture, with the few other survivors they come across no longer being quite as sound of mind as they may once have been.
This is the primary setting of Men. The world population is reduced to ONE, then back up to eleven, before the main plot takes place. Unfortunately for the human race, all eleven of those people are men. Fortunately for the human race, they don't age and are Made of Iron.
Metro 2033 and the eponymous game take place 20 years after a nuclear holocaust. The only survivors (that we know of) inhabit what used to be the Moscow Metro with various stations being city-states on their own. Factions have sprung up, and death is around every corner. Going to the surface is a death sentence.
Mike McQuay's Pure Blood and Mother Earth, which involved North American culture devolving into feudalism and the use of giant dogs (inexplicably renamed "woofers") as mounts.
The Newsflesh trilogy, set 20 years after the Zombie Apocalypse. Humanity's survival is credited to George Romero (for making lots of people Genre Savvy) and bloggers (who immediately reported the apocalypse at face value, while traditional media initially wrote it off as an elaborate prank or something).
The Night Land is set 20 million years in the future, where the Sun has guttered out and died, leaving Earth in utter darkness. The few remaining humans live in a vast pyramid, while the outside is uninhabitable and overrun by Eldritch Abominations.
Sergey Lukyanenko's Nuclear Dream novel takes place in what used to be the US after a nuclear holocaust. Most survivors remain in bunkers, fearing the harsh life on the surface, where only people who call themselves "dragons" (by rejecting all that makes them human and looking out only for number one) can survive. The protagonist's goal is to try to prevent a delayed launch of a nuclear missile at an unspecified enemy.
Nevil Shute's On the Beach follows the short lives of people living in southern Victoria, Australia, after the rest of the world has blown each other to bits with nuclear bombs. Everybody dies, All of them. Yes even the baby. And the dog. They all die. Incredibly depressing, but still a brilliant book.
The One is a depressing and physiological story about a 13-year-old girl who is the only one left in her town after a deadly flesh-eating parasite kills the entire population and is forced to find a cure for it. She wasn't the only one left in her town, her friends had the parasite as well, but since she was one of the last ones affected, they didn't trust her any longer and left town.
William R. Forstchen's One Second After is a Cozy Catastrophe that begins with an EMP attack on the US and tells what happens in the followingyear.
The Passage by Justin Cronin has this in spades, due to a Depopulation Bomb resulting in rampant vampires wiping out most of the American Continent.
The Pelbar heptalogy by Paul O. Williams is set in North America 1,000 years after a nuclear war, describing how the communities along the Heart River (formerly the Mississippi) are trying to reforge anything resembling a nation.
In the Pendragon novel The Pilgrims of Rayne, Bobby discovers that the tropical island paradise of Ibara is actually part of Veelox, after three hundred years have passed since Aja Killian's time. The rest of Veelox is a crumbling wasteland and the people not living in Ibara aren't much better than animals. In Raven Rise, Third Earth could probably also fit this trope well.
Julianna Baggott's Pure is set after a nuclear event that leaves many people fused to whatever they were near before the blast, be it objects,animals or other people. The titular 'pures', who are unharmed, live inside domed cities, while the others struggle to survive outside.
M. P. Shiel's 1901 novel The Purple Cloud finds a man returning from a Polar expedition to discover that seemingly all other humans and animals on the planet have been killed by the purple cloud of the title.
Russel Hoban's Riddley Walker is an example of this, as it takes place roughly 3,000 years after an apocalyptic event which left England in an Iron Age existence. Civilization as it is has been reduced to a mere shadow of what it once was: common religion is based on Punch-and-Judy shows, what metal supplies remain have to be salvaged from ancient ruins, years marked AD are said to stand for "All Done", and the English language is, if the narrator is to be relied upon, now written phonetically (making the book incredibly difficult to read without speaking it out loud).
Cormac McCarthy's The Road takes place after an unspecified event that not only leaves humanity nearly extinct but has destroyed the atmosphere such that nothing will grow.
His first full-length novel, This Immortal (which was originally serialized as ...And Call Me Conrad) deals with an immortal man who lives long enough to experience this.
Damnation Alley deals with a journey through a post-apocalyptic wasteland (just about the only detail it has in common with the cheesy movie that is supposedly based on it).
In David Weber's Safehold series, the planet Safehold is humanity's last desparate attempt to evade genocide at the hands of the Gbaba. It's a foregone conclusion that every human world except for Safehold itself has been wiped out.
Saturn's Children by Charles Stross explores a Solar System inhabited only by robots centuries after the mysterious extinction of humanity.
R. Scott Bakker's Second Apocalypse takes place two thousand years after the First Apocalypse. Large parts of the continent are still wasteland.
The setting of Septimus Heap is implied to take place long after the end of our world.
Syren has characters discuss old stories about men flying to the moon in white tubes. Later, a relatively modern submarine is encountered, and a tower holds what seems to be a modern elevator, with a light that shows a down-pointing arrow when you, well, go down. The books also talk about Roman temples, and make constant references to real world places, like Peru, China, and Persia.
Fyre adds more fuel to the, er, fire of this theory. Septimus writes the date on the snow outside the House of Foryx. It's... quite surprising, to say the least.
Jasper Fforde's Shades of Grey takes place five hundred years after "The Something That Happened" which wiped out the Previous civilization. What that Something was is a mystery.
Terry Brooks'a Shannara series is set after the Great Wars have dramatically altered the landscape and reduced civilization to medieval levels. Gnomes, dwarves, and trolls are mutant humans. Elves are real elves, having come out of hiding after the war.
The Shattered Sea is set in a Norse flavored Standard Fantasy Setting which has been built on the ruins of a precursor "Elf" civilization which destroyed itself in a cataclysmic war and split continents (hence the series title). It's made increasingly clear throughout the series that the story's setting is Earth All Along and the cataclysm in question was a nuclear war. It's also suggested that the books are actually set in the relatively close future/civilization fell only recently, given that technology still works and some areas of the world are still irradiated.
The Shattered World and The Burning Realm are fantasy novels set a thousand years After the End of a world that got broken into fragments. Desperate damage-control by the resident mages has preserved the fragments in a vast envelope of air, and equipped all the pieces big enough for settlements with Runestones that provide gravity and a regular orbit. Unfortunately, the Runestones' magic is almost exhausted, making these both After the End novels andJust Before the End novels.
Skylark by Meagan Spooner is supposedly after a nuclear war which wiped out most animal species and most of human civilization.
Perri Rhoades' Spectral Shadows has Serial 11, which takes place "At the End of Time" on the planet Cygnus, where the Funny Animal People that live there now were the result of apocalyptic genetic warfare by the humans.
Alfred Bester's seriocomic novella "They Don't Make Life Like They Used To" features the last man and woman on earth — at least, they think they might be — trying to carry on with their daily lives in a decimated midtown Manhattan.
The To The Stars Trilogy by Harry Harrison is set a few centuries after a peak oil crash and subsequent world chaos.
The Towers Trilogy takes place after an event called the Fall, which wiped out modern civilization and caused a Magitek-based society to rise in its wake. The wealthy live in giant Mage Tower skycrapers which float above the devastation, while the poor are forced to scrape out a living among the ruins on the ground.
Ardath Mayhar and Ron Fortier's cheesyTrail of the Seahawks. Also involved North American culture devolving into feudalism and the use of giant dogs (quite explicably called "riding dogs") as mounts.
The Tripods series by John Christopher deals with a post-alien invasion future where the only humans not turned into zombie-like slaves are young children.
The Uglies Series, by Scott Westerfield, features a world where nothing using gas works and apparently humanity's population is reduced and controlled, and segregated into the eponymous Uglies, and Pretties ( And Specials.)
Harry Turtledove's Valley-Westside War is set in a fairly typical post-nuclear world. The twist is that it's set in an Alternate History (this is a Turtledove story after all) where the war happened in 1967 and the protagonists are scientists from a future history where travel across alternates has been discovered who are studying the world to see how and why things went wrong.
The setting of Who Fears Death is implied to be this. There is technology, but it's mostly decayed and in disrepair. According to the Great Book, the Okeke created a great technological society, but were crushed when Ani woke up to discover what her creations had done and created the Nuru to punish them.
Wool takes place after something devastated the entire planet and people must live in underground silos to stay safe from the incredibly toxic atmosphere.
World Made by Hand, by James Howard Kunstler, is set in a future where industrial civilization has collapsed simply from petroleum depletion and resultant stresses on socioeconomic systems .(Terrorists also destroyed Washington, D.C., and Los Angeles with nuclear bombs, but there was never any all-out nuclear war.) This is one of a fairly new genre of post-oil novels.
Clark Ashton Smith's Zothique is set 8 million years in the future, when the Sun is dying, civilization has long since collapsed, science has been forgotten, magic has returned, and humans are going extinct.