The Esperanto comic book 10 Jarojn Poste ("10 Years After") is set after a devastating nuclear war; the subsequent plague of male sterility, from which only a few men are immune, threatens humanity with extinction.
Age of Apocalypse, needless to say, takes place in a world where Apocalypse has taken over North America, and turned it into a massive Crapsack World basic on his Social Darwinist beliefs. The rest of the world isn't any better, with Brazil destroyed by nukes, the Middle East oilfields also nuked, Japan also decimated, and Central America gone.
The End League: Post apocalyptic superheros who suck really hard at what they do.
The upcoming Godzilla IDW comic, Godzilla: Cataclysm is set in a Mad Max-esque world where humanity is on the verge of extinction due a Kaiju apocalypse.
Hex, the follow-up series to Jonah Hex, had Hex transported to a Mad Max style 21st Century Earth following a nuclear war.
Judge Dredd is set after the nuclear apocalypse where outside of a few giant city-states (and a Lunar colony, for some reason), the entire world is a barren radioactive desert filled with bizarre mutants. Society has managed to survive but the situation has gotten progressively worse since then, with several Mega Cities wiped out in wars or other catastrophes, including Mega City One itself being reduced to a fraction of its size after a viral outbreak.
Just a Pilgrim is set in a world where the sun went nova billions of years early. The Earth's a barren desert waiting for the sun to burst.
Kamandi's world later became the setting for a bevy of other post-apocalyptic DC comics that got lumped in with it when they were incorporated into The DCU, including the Atomic Knights, Hercules Unbound, and Hex.
Hex actually emerged in a separate Post-Crisis apocalypse that was confirmed to be survivable by later accounts. OMAC was later retconned to be the prequel to this world, while Atomic Knights and Hercules Unbound were majorly retgonned by later accounts.
Killraven was set in a world where the Martians from The War of the Worlds came back in the '90s and won this time. It focused on one of the few free human rebels and his attempts to overthrow the alien scourge.
Kingdom takes place after most of humanity has been wiped out by a race of Big Creepy-Crawlies known only as Them, and the majority of the survivors are in Suspended Animation in Antarctica (and possibly New Zealand).
In the French comic Les Eaux de Mortelune (The waters of Deadmoon), most of humanity is wiped out or has degenerated into grotesque mutants hunted for their meat. Pockets of humanity remain in places (such as Paris, renamed "Mortelune") where they have both the technology and the fuel to purify the toxic water, and buildings that can resist to acid rains, but it is later revealed that Lyon is now inhabited by giant flies, Avignon by giant termites and Les-Baux-de-Provence by giant telepathic praying mantis. All three races are actually more advanced and way more prone to long-term thinking than what's left of humanity.
The Luther Arkwright story For a Few Gallons More in parallel 02.79.10 is set in a world where civilisation collapsed after a bacteria with a psychedelic effect was released after an attack on the research institute. The only people who survived the prolonged and massive psychedelic experiences where those already used to psychedelics.
Old Man Logan is a Marvel story that takes place in an alternate timeline where all the Supervillains banded together and took over, turning the world into a wasteland.
Scud the Disposable Assassin: Not until late in the series that we learn the rapture began not long after the release of Ghost Busters 2 and has been going on ever since because the Devil was usurped by a mechanical stuff-collector named System. There weren't any raging wars or apocalyptic scenarios, but there was an influx of supernatural creatures, black magic, random mutations, and intergalactic alien businesses opening up on earth. Society is the same but a little more messed up.
In the Sonic the Hedgehog series by Archie, the world of Mobius is actually Earth ten-thousand years later, and Mobians the result of the alien Xorda's gene bombs - which wiped out most humans, mutated most of the surviving humans into Overlanders, and created the Chaos Emeralds - mixing human DNA with animals.
And then there's the time Silver comes from (200 years in the series' future), where an unexplained disaster has completely destroyed the world, except for a few isolated pockets of civilization.
Storm : the main character is transported to a far future where civilization has fallen and rebuilt several times, and is currently quite primitive. He helps rebuild, and then promptly time travels again to a yet further future where society has again fallen.
Every Superman story, perhaps especially those dealing with other survivors, such as the floating city of Argo, the bottle city of Kandor, etc., is set After the End of Krypton.
V for Vendetta is set in a world that was almost completely destroyed by a nuclear war, presumably only the British Islands are still intact; it's mentioned at one point that "there is no Africa any more".
Wasteland, by Oni Press, takes place after some unspecified disaster called "The Big Wet".
Y: The Last Man is a comic series that takes place in a world where a biological event has wiped out half the mammals on Earth; specifically, the males. The main character and his monkey, plus a few exceptions, are the last living Y-chromosome carriers, and since our protagonist's fiance was in Australia at that time and he's still loyal to her, things are nowhere near as rosy as that scenario might suggest. The civilization of the world falls into chaos as infrastructure and industry collapse (not so much because women can't run things, but because there aren't enough of them, and fewer with the necessary training) but, a few years into the series' real-time run, the all-female society has more-or-less started to function again.
The DC comic miniseries Me and Joe Priest postulated a lower-key version of Y, with all human males (save the eponymous cleric) and most human females losing the ability to sire children. Much like Children of Men, the population largely gets older and older and waits to die.