Europe and Asia after the plague of 1347-1350, otherwise known as The Black Death, the Great Mortality, and the Year of Annihilation, is as close as human history has ever gotten to After the End. The continents' populations were at a high, with population growth slowing down in the preceding decades as the land was stretched to its sustainable limits. When the plague hit, it struck at a time of relatively high population density and malnutrition, the death rates ranging from 15% to over 60% from area to area. Though very little of the population - 10% is a common figure - lived in towns and cities, these were the places that got the worst of it and many were almost totally depopulated as people died or fled. In Europe it dealt a heavy hand to the nobility, the Church and higher learning in general. The relative scarcity of the peasantry meant they were in a much better position to negotiate their working conditions and wages, at the expense of the nobility. Pre-plague, most literate people were clergymen and nearly all clergymen were literate; clerical literacy did not reach pre-plague levels until the sixteenth century, with the advent of printing and a concentrated programme of Clerical and general education. Furthermore, the devastation of the plague and the resultant social upheaval cultivated rebellion, religious fanatacism and anarchy (such as the anti-Semetic, anti-authority flagellants). Even before the plague, the 14th century had been a crappy time to be alive and European what with the Hundred Years' War (which wasn't too bad, actually), the Mongol Invasions (which actually were rather bad), various natural disasters, and the years of crop-devastating heavy rains (rain encourages fungi, which at its best reduces your crop yield and at its worst kills you when you eat your bread) that preceded the plague in some areas.
It was no coincidence that the Pilgrims chose Plymouth as the site of their colony. It turns out Plymouth was an empty Indian settlement. The Pilgrims arrived just shortly after a massive smallpox pandemic had swept the area, which wiped out over 90% of the Native American population. Instead of trying to eke out an existence in the untamed wilderness, they took over the empty Indian settlement and its surrounding farmland and infrastructure, even going as far as opening the recently-dug graves to search for anything useful to salvage. In addition, what little remained of the local population was in no shape to seek any fights with the newcomers. Some people have speculated that the American Union's fascination with post-apocalyptic scenarios has its origins in these first, formative years.
Plymouth wasn't the only such location. We now understand that the American continents were teeming with people, that there were multiple, vibrant civilizations. Plague after plague swept through, literally and repeatedly decimating populations. That we know so little about many native cultures and histories is do in no small part to the fact that 2/3rds of their populations died. Everything since the arrival of European invaders has been After the End for Native Americans.
The period of European history between the fall of Rome and the rise of Charlemagne is sometimes called "The Dark Ages", and said to be characterised by doom and gloom. This is somewhat of a misnomer created by Renaissance scholars, who were such Ancient Greece and Rome fanboys (well, mostly fanboys) they didn't think a period without classical knowledge could be anything other than post-apocalyptic (Petrarch, the father of Renaissance humanism, said "What, then, is history but the praise of Rome?"). In truth, a lot of classical knowledge was lost, but it was more on the order of "we can't build classical-style ampitheatres anymore" than "devastated world of crap". It wasn't that horrible most of the time, save for Viking and Magyar attacks. And the constant border wars that came with the political fragmentation - not, of course, that the last centuries of Rome hadn't been marked by this sort of thing - and the rise of the armed aristocracy. And 30 and 100 year long wars, albeit ones which didn't really affect the wider population too much. And serfdom, which was always a bit of a downer if you weren't a noble or a clergyman (but is a big step up from the slavery system of Rome).
Classical civilization continued unabated in the Eastern Roman Empire (the "Byzantine" Empire). "The Dark Ages," a misnomer as it is for western Europe, did not exist as far as the eastern Romans were concerned. In fact, Greek scholars steeped in classical learning migrated to western Europe after the fall of Constantinople and made a significant contribution to the Renaissance.
Just the same there certainly was a period of time for a fairly substantial number of people in Western Europe where they no doubt looked up upon crumbling Roman ruins and realized that life used to be better and civilization a grander thing than what they had access to themselves. Just try to imagine hunkering down for months of European winter with all your relatives in a shack and not only do you not have any sort of modern entertainment but you're illiterate too. Not that there's a book within twenty miles - a day's cart ride, and the average distance from any given village to a 'market town' - anyway.
China after the Xinhai Revolution, with No More Emperors and all. Simultaneously a period of great political and social chaos and coupled with huge progress and massive muck-ups in culture and economy.
Today, Hiroshima and Nagasaki are thriving... but this is because the bombs used were for shock and awe rather than sheer destructive power, were detonated in the air, (and so didn't leave significant fallout) and were very small in nuclear terms (15kt for Little Boy and 20 for Fat Man). For comparison, the most recent North Korean nuclear test was of a similar yield and the intelligence community debates whether it was nuclear at all.
Actually, the North Korean Nuclear Tests had bombs gauged about 6 kilotons or less. Far less than the Little Boy and Fat Man bombs. And nowhere near as powerful to destroy cities or cause significant fallout.
The fire-bombing campaign was more on this order. In one particularly spectacular attack, 40% of Tokyo was razed in a single night. It killed at over a hundred paces and left virtually nothing in its wake.
The early Triassic Period, which followed the PT Event, the greatest mass extinction in Earth's history, and the Paleocene Epoch, which followed the KT Event, the second greatest mass extinction, wherein, among many others, the dinosaurs were wiped out.
The Cretaceous-Tertiary Extinction was not the second greatest mass extinction, only the most well known one. In fact, most of the extinction events from the beginning of the Permian through to the Triassic-Jurassic Extinction actually saw more species wiped out. Think about that.
Actually, the entirety of human history has happened after the end... of the dinosaurs. That's right kids, we live in a post-apocalyptic world.
And the dinosaurs themselves lived after the end of the Permian-Triassic mass extinction, so you could say the dinosaurs themselves lived in a post-apocalyptic world.
There is evidence that the entire solar system is cobbled together from chunks of other solar systems blown apart by supernovae which, given the age of the universe, were probably made from other systems and so forth. In fact the Milky Way itself is probably a new system made up of older galaxies which in turn were made up of the remnants of quasars and so forth and so on right on back to the big bang.
In reality, the worst "cosmic" tragedy to have any feasible chance to affect mankind at all is localized space junk affecting just our tiny planet, and even then, it will in all likelihood be detritus from objects we ourselves put in orbit coming back to bite us in the collective ass. Hazardous microscopic trash hurtling through stable orbit above us at ludicrous speeds, destroying at random some satellite we put up, and chunks thereof exponentially multiplying the threat to further man-made craft sent into or passing through orbit, eventually "grounding" us and our further ambitions and creations entirely, as per the anime Planetes. Possibly... The plots of Deep Impact, Armageddon, etc.? Unlikely. Galactic or universal catastrophe ever reaching out as far as to affect anything still recognizable as a continuation of humanity? Impossible. Even if we were in fact obliviously living After the End of a new, latest Big Bang, even if it had already extinguished 99% of the celestial bodies whose delayed, ancient light is reaching us just now, neither humankind nor any other current species on Earth would ever be long-lived enough to still endure to a time when such hypothetical destruction arrives to any point close enough to affect us. Fact.
This is basically the backstory behind the movie Gravity.
Our Universe is in a sense living After the End. Eternal Recurrence-like ideas as those commented below apart, the very early Universe just after the Big Bang was one very different, exceedingly dense and hot where the four fundamental forces of Nature were merged into just one. Whatever had existed by then would have faced said "superforce" dividing into the ones we know and the Universe cooling and becoming less dense as it expanded, with cosmic inflation if it had happened being the "coup de grâce" for that.
Humanity may have come very, very close to extinction, multiple times. There's the Toba catastrophe theory. Shortly put, our numbers were reduced to around 10-15 thousand individuals due to a volcanic eruption around 70,000 years ago. In addition, humanity can be genetically traced back to a mere 50 women. That means that there was once a time when only 50 women (and an unknown number of men) were the only survivors of something that nearly made humanity extinct. We are the result of their "after the end."
It's just as possible that there were many more others alive and we simply didn't inherit their genes. Regardless, there are some evidences (such as the Toba theory above) that the human race did go through a population bottleneck of some kind very long ago, either because of a major global disaster or simply because a small group managed to pass their genes along to the present population while the others failed to do so for more mundane reasons.
One cosmology theory holds that the universe continually expands (Big Bang) and then eventually contracts (Big Crunch), destroying everything before another Big Bang starts the cycle over again. If the theory is correct, literally everything in the (current) universe is "After the End" of an untold number of previous universes.
Seems to be ruled out in favor of the Universe expanding into oblivion (Big Freeze). However after a very, really, long, time, a new Big Bang could appear from that nothingness (Roger Penrose has a similar idea on his book Cycles of Time: An Extraordinary New View of the Universe). That short of some theories that suggest the formation of a black hole could give birth to a new, independent Universe via a Big Bang.
The Greek dark age of 1200-750BC could be argued to fall into this category, with a widespread collapse in Bronze Age civilization.
For those of you wondering what this is, something happened at the end of the 13 century B.C that caused the end Mediterranean Bronze Age civilization to collapse including the Mycenaeans, Hittites, Canaanites, Minoans, and greatly weakened Egypt. Its said to be worse than the collapse of the Western Roman Empire and often cited as the worst case of societal collapse in human history. It inspired the Iliad and Odyssey, and some of the early books of the Bible. The weirdest thing is that scholars have almost no clues as to what happened. Warfare is often cited as the main culprit, but more evidence points to that and fragmentations within those societies and natural disasters. Nobody really knows what happened, however.
One of the (many) factors that contributed to the great success of the Muslim Conquest is that it happened After the End of the war that exhausted both Byzantium and Sassanid Persia. By that time, Persia was a mere shade of its former glory, they couldn't even mount effective resistance against the newly-emerging bands of Arab raiders, and while the Byzantines survived, they were reduced to a Vestigial Empire, albeit one that hung on and even experienced resurgences for the next eight centuries.
A widespread viewpoint in 17th century Russia. The century started with several lean years in a row, caused by abnormal colds. The resulting famine killed two-thirds of the population. The tsar was overthrown and a decade of coups, civil wars and foreign invasions followed ("Uncertain Times" or "Times of Trouble"). The order was somewhat restored under the newly elected Romanov dynasty, but life wasn't easy. When schismatic priests in the 1660s declared that the end of the world is happening and the country is ruled by the Antichrist, people tended to agree.
And as the people of Russia have somewhat got used to the church reform... came Peter the Great. Who had promptly introduced his subject to such horrible things as foreigners, shaving, tobacco, foreigners, regular army, "Hungarian" (aka European) clothing, "assemblies" (parties for aristocrats with royally mandateddebauchery, drunkedness and all sorts of shenanigans)... and did I mention foreigners? Add to this quite a few wars and you can understand why so many people beleived that the end of the world has already happened. Peter was called the Antichrist repeatedly. His abolition of Russian Orthodox Patriarchy (and requisition of church bells to be melted and made into cannons may have helped the sentiment a wee bit...