Gamma World is set on an Earth which, centuries after some ill-defined global catastrophe, is populated with mutants of every mental and physical stripe, sentient animals and plants, insane malfunctioning robots and humans. The players are strongly encouraged to not take this very seriously. The RPG credits Lanier's Hiero books, Aldiss' Hothouse, and Andre Norton's Star Man's Son as influences (see Literature).
For humans, we have the Age of Strife at the end of the Dark Age of Technology, where after defeating the soulless robots called the Men of Iron, humanity fractured into a million states before the God Emperor of Mankind came and restored order; the Horus Heresy at the end of the Great Crusade, where fully half of the human race turned to worshiping demons and wiping out the other half, ending with the rebellious Horus dead and the Emperor on life support; the Age of Apostasy following the First Age of the Imperium, where the mad Goge Vandire drove the Imperium into self-destructive religious madness; and, arguably, the Time of Ending, which is going on right now. After each one, humanity recovered; after each, the recovery was less complete, and society became worse. There are quite likely at least a few apocalypses that have simply not been named.
There have been at least several other apocalypses involving other races going on: the most recent and significant must be the fall of the Eldar, although there is the apocalypse that wiped out the Old Ones as well. In fact look at any race and you'll find an apocalypse or two somewhere in their background (though with Chaos and the Tyranids they were usually CAUSING them).
The Tau were on the brink of wiping themselves out in a civil war called Mont'au, or "the Terror", before the mysterious Ethereal caste appeared in the eleventh hour to get them to work together. Not a mean feat, considering their best weapons at the time were pikes and black powder cannons.
The Orks have fallen from a previous state of civilization, having inadvertently destroyed their Brainboy leaders and descended into murderously happy anarchy.
BattleTech (Although the 'end' happens after humans have colonized space).
Battle Tech has had a few Apocalypses:
The fall of the Star League and the resulting 1st and 2nd Succession Wars which bombed the galaxy back to the Stone Age (barely 20th century tech, with how to make mecha and starships all but lost, though not how to repair them)... this was followed by 2 more wars lasting 300 years all together although these were low intensity conflicts because of the damage inflicted earlier.
The Word of Blake Jihad, a deliberate attempt to once again bomb the inner sphere into the dark ages, costing several TRILLION Lives over a 13 year-long war. Planetary saturation nuclear orbital strikes were common.
Exalted takes place after 3 different Ends, and is set at the End of an Age. First was the Primordial War (named after the Primordials, the creators of the universe, who lose), involving the extinction of scores of civilizations and races; most of Creation was burned up by a sore loser's last act before surrendering. Then the First Age, which was ended by the Usurpation. Lastly, a plague made by a ghost of a Solar killed in the Usurpation killed 90% of the population, and was followed by a invasion of The Fair Folk, who succeeded in unmaking half of Creation (by area).
The good news? You play as the eponymous Exalted. They can do anything, including flattening the Fae and pushing them back to reclaim parts of Creation from the Wyld, and in the past they beat down the creators of the Gods themselves. The problem is that the forces of the Underworld have Exalts too, and then there's that Great Curse the Solars suffer, which slowly turns them into crazy tyrant-demigods. The potential to fix the world is there, it'll just take a lot of work, and the Exalts overcoming the effects of the Great Curse along with every possible threat to Creation... but if anyone can do it, they can.
Palladium's flagship title, Rifts, takes place a couple centuries after the apocalypse. On midnight of the Winter Solstice in the year 2098, two nations in South America engaged in a brief exchange of nuclear weapons, killing several million people. The sudden death of so many people, combined with the mystic timing of the event, caused the Ley Lines crisscrossing the Earth to surge with a power unseen since the disappearance of Atlantis. This caused a number of weather anomalies across the planet which caused more deaths, fueling the ley lines even further, resulting in a chain reaction of death and increasing magical power. Eventually, the magical level rose to the point that the ley lines started becoming unstable, causing the eponymous Rifts, holes in time and space, to tear open and pour forth aliens and monsters, causing even more death. By the end, 60% - 80% of the Earth's population had been wiped out, leading to a Dark Age that lasted roughly a century, where humanity clawed its way out of the chaos and horrors caused by the Coming of the Rifts. In the main setting, Earth is now a dimensional hub where magic and technology exist side-by-side, sometimes peacefully, often violently. Humanity has regained a few footholds here and there, alongside aliens and other creatures who are as much victims of the Rifts as the natives, trying to eke out an existence on a world gone mad.
The supplement Chaos Earth takes place literally the day after it happens.
Paranoia is set after a nuclear war... or something... known as the Big Whoops, which ended with The Computer ruling over a huge population living underground in Alpha Complex which may be a dome city.
If the High Programmer book is to be believed it's San Francisco that's domed and underground, because a really big rock (or something) was going to hit the Earth, then commies took over the world
It's intentionally vague, but the main constant is not available at your security clearance, citizen.
According to the second-edition corebook, humanity retreated into the underground complexes to avoid a giant asteroid. Alpha Command, the computer that took care of day-to-day issues in human civilization, was damaged during the impact, and much of its data was lost. When it tried to boot up protocol files, it found an old '50s defense manual and assumed Communist sabotage, which it transmitted to the computers in charge of each complex - starting with Alpha Complex.
Earthdawn is set on Earth after a devastating invasion of other-dimensional Horrors wiped out most living things on the surface and mutated what was left. The Horrors (mostly) returned to their home plane after the level of magic dropped too low for them to stay, allowing the survivors to re-emerge from their retreats and begin to repopulate the planet.
Shadowrun is set in the future of Earthdawn, in 2070 our calendar, after a series of nasty magical cataclysms and wars (including a war between all the major continental European powers that ended with a massive nuclear airstrike on every nation's entire command structure by (presumably) England) and other disasters that created the politically-divided megacorporation-run Crapsack World it is.
The GURPS supplement Reign Of Steel depicted a post- Robot War setting where Earth is divided up and ruled by eighteen artificial intelligences and the human population is just 37 million, most of which are either in slave camps of one sort or another or are hunted like wild animals in the wilderness. The catchphrase: 'The war is over. The robots won.'
Also an invaluable resource for post-apocalyptic GURPS gaming is GURPS Y2K, which takes a long look at the fears of the turn of the millennium and the post-apocalyptic (or straight-out apocalyptic) scenarios that would develop.
The Day After Ragnarok, a setting book for both Savage Worlds, Hero System, and now FATE Core. The Nazis managed to pull off a summoning ritual that pulled the Midgard Serpent into our reality, but before it could fully manifest an American suicide team loaded the Trinity Device into a plane, rammed into the Serpent's eye, and detonated the bomb. The flailing around of a gargantuan serpent (whose head alone is 350 miles across) in its death throes while dripping magical radioactive snake venom from its fangs crushed most of western Europe and northern Africa.
Mutant Future is a close-as-you-can-get-it retroclone of post-apoc RPGs such as Gamma World using the Labyrinth Lord rules.
Aftermath! is an old Scavenger World game, and it's slim pickings since it's a few generations after the end. There's lots of scenarios for the setting, lots of little rules systems for simulating special cases, lots of genetically engineered life forms and Schizo Tech and you are as likely to die of starvation and exposure as violence.
Legend System's Hallow setting is built from the remains of a solar system, with floating islands powered by living engines (called angels) keeping everything running.
Apocalypse World takes place roughly fifty years after some sort of apocalypse. A suggested overarching goal for the characters is finding out what caused it and seeing if they can fix it, or at least move it from a Crapsack World to a Cosy Catastrophe.
Microscope A game can be built around this theme, or it can be a blip in game time as a city is destroyed in a single turn.
The third edition of Traveller, the New Era was set after the destruction of interstellar cvilization by a massive Civil War followed up by the release of a homicidal Computer Virus superweapon. The death toll was in the trillions.