Warhammer 40,000. It never got better. Warhammer 40000 is just one long love poem dedicated to this trope.
An appropriate example: The Eldar. Once rulers of a galaxy-spanning empire whose technology had relieved its every citizen of all need for manual labour, given them the ability to move planets "to get a better view", and extinguish stars, they descended into anarchy amidst an orgy of cultish violence and depravity, destroying their empire and much of their civilization. Then it got worse: The combined lust and excess of the species coalesced in the Warp to spawn a new Dark God, destroying their homeworld, everything around it for about fifty light-years and submerging the entire region in a Warp-realspace overlap where Daemons play amongst the ruins of the lost Eldar civilisation.
Then it got even worse: That new dark god eats Eldar souls for breakfast, literally, and consequently hunts down and destroys the few survivors wherever possible. Oh and then the Humans grew to fill most of the power vacuum, and also want to hunt the last dregs of the Eldar to extinction. This isn't anything personal though; the Imperium feels that way about all sentient alien species without fear or favour.
And now the Necrons, who the Eldar were just barely able to defeat at the height of their power, have started to wake up again. Of course, the Eldar are on the verge of extinction, so they have no hope of defeating the Necrons. On top of that, their old foes the Dark Eldar, Orks, and the forces of Chaos are on the rise, and a bunch of extra-galactic bugs are barging into the picture as well. If the Eldar decided to ally with the Tau and those hairy mon-keigh (fun fact; "mon-keigh" doesn't mean "human", it means "those who must be exterminated"), they might be strong enough to defeat one of those threats...and of course, instead of forming an alliance, the nominally "good" guys are still trying to kill each other.
Actually, 3rd edition. Back then losing a hundred planets in a day was considered winning, chaos cults were rampant on earth, the high lords were mentally insane, and space marines were definitely evil nut jobs bent on purging humanity of even the slightest imperfections, sometimes even killings a planets communications ability in a process if not the majority of the population outright. 4th and 5th are MUCH nicer places to live. At least now suicide isn't the better option.
The 4th and 5th Editions did indeed seem to be making the universe nicer, if only because there was more room for glorious heroes rather than everything being hopeless, all the time, forever. Oh wait, what was that about hope? Yeah, now 6th edition is out. More Necrons are awakening, and now we learn that they're not the mindless remnant automatons of near-extinct star gods, because their leaders are waking up and they're just as genocidally psychotic as anyone else; the Tyranids are encroaching in ever larger numbers, and they're popping up far more often "inside" the galaxy which points to the fact that they're coming from above/below the galactic plane as well; Abbaddon the Despoiler has suddenly grown competent; and the Astronomican - the great shining beacon lit by the Emperor's will (and the soul-shredding efforts of a thousand psykers) - is not only what's ATTRACTING said Tyranids, but after ten thousand years the Golden Throne that channels the energies is starting to break down, and the Adeptus Mechanicus doesn't know how to fix it. If that fails completely, interplanetary traffic will all but cease, astropaths (psychics which allow inter-planetary communications) will likely lose their controlling focus as well, and the Age of Strife which splintered humanity once before will seem like a weekend trip to the beach.
Planetary example: Valhalla was a verdant Imperium paradise until a comet struck the planet. It hit and boiled its oceans, causing a pall of dust to block out most of the sunlight, and managed to knock the planet out of orbit - the planet became a frozen wasteland where its people lived underground, struggling to survive... and then Orks invaded. The Valhallans eventually managed to erase the Orks from their world, leaving their Imperial Guard regiments raised to this day famous for stoic determination and hatred of Orks.
An inherent part of the Old World of Darkness series, especially Vampire: The Masquerade and Werewolf: The Apocalypse. To take an example from the backstory of Werewolf, first the spirit of order went crazy. Then the essential spirit responsible for turning ordered matter into energy was imprisoned, dooming all natural things to a slow death as the very essence of creative energy within the universe ran out. Then little pieces of said spirit oozed through the side of the cage, driven mad in the process, dropping into the material world like radioactive, acidic, mind- and soul-devouring monsters. Then the central spirit itself started breaking loose like its pieces did. Those who peek into the cage are driven mad by the exposure, able to do little more than mewl softly and attack the sane. There's a reason that the game had an "End World Now" button.
White Wolf kicks it up a notch with the newer Age of Sorrows, in which Exalted takes place. Exalted are reincarnating god-men who were cursed by Primordial divinities (whom they killed basically out of spite) with rampant, uncontrollable excesses and vices born of their primary virtues. Insane, aggressive, and powerful god-men are bad. The lead, biggest 'n baddest Exalts, the Solars, were exterminated for their madness in the bloodiest war existence could comprehend (at least since the Primordial War). Their usurpers, the Dragon-Blooded, drastically decayed reality because they couldn't hold it in place as well as their superior dead brethren could. At the time Exalted takes place, the once-dead Solars have been reincarnating, and are pissed off. Making this situation worse, the world has Eldritch Abominations galore surrounding the entire world and about half the mighty Solars became liquid evil death and are working under 13 pseudo-gods (who in turn are commanded from beyond the grave by the Primordial beings slain in the beginning) with the ultimate goal of ending reality. Really, was living under the rule of some prick Primordials all that bad when compared to how It all Got Worse?
The setting of Exalted has the following It Got Worse moments. Total chaos of omniexistence -> Primordial assholes create the world as a vacation spa and play Cosmic Xbox -> their servant Gods create the Exalted to beat up said Primordial assholes and take over the Cosmic Xbox, leading to said Exalted getting cursed -> The most powerful Exalted go nuts after centuries of raw power and cursed madness, and are put down by their brethren -> The weakest of the Exalts are set up as a puppet government, but HEY LOOK a plague that wiped out 90% of the world's life (yes, all of it). Oh, and hey look, the chaotic monstrosities from way back are coming to wipe this ugly "reality" out of existence. -> Luckily, one woman gets access to the ultimate superweapon, stops the baddies, and sets up a brutal, corrupt dictatorship with her decadent, incestuous descendants. -> Said woman goes missing, sending her sprawling empire collapsing in a planned obsolescence tailspin of civil war and backstabbery. -> Hey look, the Solars are back. Except 2/6s of them now work for the dead Primordial assholes who want to cast everything into a Void so they can finally stop suffering. And another 1/6 are the private buttmonkeys of the Primordial asshole survivors they imprisoned. In the flesh of the enemy leader. And those ineffable chaos things? They're hungry, too. And all of the Exalted are busy plotting to kill each other "for the greater good." The Gods are either corrupt or jaded, except for the ones hopelessly addicted to Celestial Crack. The setting's Prometheus is comatose and dying (of robot cancer) and his children are invading to steal magical metals and souls to feed him... what else? Oh, right. The Exalted are all still cursed. (Including the ones who have the best shot of seeing what's going on. Their curse turns them into micromanaging JerkAsses who make epically critical blunders and can never learn from their mistakes — and get worse when they work together.) Take that, Warhammer 40k.
And it still gets worse. Any of the Exalts in service to the dead Primordial assholes who goes rogue will build up Resonance, that provides a good chance of tainting Creation's essence and possibly wiping out a village in a massive necrotic pulse (and which adds a fair dose of Being Good Sucks). The ones in service to the imprisoned Primordial assholes eventually have to pull off arbitrary acts of villainy to appease their rather cranky patrons. One of the 13 evil undead demigods might well be the soul of the very worst of the First Age Solars. The private buttmonkeys of the surviving Primordial assholes are turning themselves into more Primordial assholes. Oh, and that MIA woman who saved the world with the ultimate superweapon? She's married to the nastiest of said Primordial assholes, who has hatched a particularly unpleasant plan to dick over the entire world with her help. They still control said superweapon. Now all we need to do is give the Unconquered Sun a bad reaction to his Celestial Crack so he has to go on life support, and we've got 40K.
The origin of the monster Grond in Champion is pretty much this. While in prison, a criminal volunteers for medical experiments. But one night, they inject him with the wrong stuff. He pitches a fit, the guards throw him into a shelf of chemicals, which enter his bloodstream through cuts from all the glass. He escapes the prison, falls into a heavily polluted river, and gets struck by lightning. And they think radiation was involved too. Bloody hell. Now all they need to do is add magic and we have pretty much the entire list from How To Give A Character Super Powers.
While Paranoia is always a Crapsack World, individual missions start by describing some specific looming disaster and end by blaming the PCs — sometimes quite rightly, sometimes not, for failing to stop it, or even helping to bring it about.
The board game Arkham Horror has Mythos cards which might as well be called "It Got Worse" cards. Drawn at the start of a turn, they open new dimensional gates, release new monsters, move the monsters around the board, and count down remaining time until the Ancient One awakens and eats the world.
In the Forgotten Realms Avatar Crisis, the forced descent of all the gods into mortal bodies caused havoc with the Weave—outside of the several-mile radius which surrounded an avatar, magic was unpredictable, either not working at all, working with a quirk, going wild, or blowing up in your face. It was spellcast at your own risk. Then Helm killed Mystra...and things went entirely insane, magically.
Cthulhu Tech and its history is pretty much made of this trope. Mankind just got out of a war, only to be invaded by the Migo. The Deep Ones decide to invade parts of the surface. HASTUR gets summoned and starts his own little genocide. Humans are being transformed by an evil corporation into monsters. The best part? This is the prologue.
In the indie game My Life With Master, a character that acquires too much Self Loathing through doing the work of the evil Master will unleash a "Horror Revealed," in which things get worse for the community at large. And if it gets too bad...well, that's when the Torches and Pitchforks start coming out...
If this trope is not occurring in your Fiasco game, you're playing it wrong.
This can quickly and easily happen in a game of Pandemic. There is an infection deck that depicts various cities across the globe that have new disease cubes added in. One of the core mechanisms of the game is that, every so often, you take the discard pile, shuffle them, introduce a new card, and plop it back on top of the deck to be drawn again—which means cards that were previously infected have a greater chance of getting infected again. In addition to this, any city that gets more than three cubes of the same color outbreak, causing all surrounding cities to be infected as well. You can see where this is going: if players aren't careful, a mild case of sickness can very, very quickly blossom to a full-scale global problem. Much of the fun of the game is turning over each infection card, one at a time, with everyone hoping that it's not a specific city...and things quickly degenerate if it is.
This has been the basis of BattleTech history since about 3028 on to the next fifty years or so. In order:
The Fourth Succession War starts when Hanse Davion marries Melissa Steiner. Everyone goes to war on the night of the reception, causing more territory to change hands than the past century of fighting.
The War of 3039 takes place, which causes even more territory to change hands as well as causing significant social upheavals in Steiner and Kurita space, with nationalist groups starting to come out of the woodwork.
The Clans invade in 3050; tens of thousands die, millions become refugees, and a full quarter of the Inner Sphere is conquered by the seemingly unstoppable invaders and their superior technology and pilots.
Operation Serpent in 3057 leads the fight back to the Clans, but also sets the stage for political unrest in the Inner Sphere, culminating in the entire central portion of the galaxy becoming a war-torn no man's land known as the Chaos March.
When the Clan invasion is foiled, the Fed-Com Civil War starts. The greatest nation the Inner Sphere has ever seen continues to fight itself for more than five years of non stop conflict, costing the lives of millions and again causing a refugee crisis. The other houses don't get to capitalize on it, being either invaded in turn, dealing with the Clans, or dealing with internal political strife.
Just when the Civil War seems set to finally end, the Word of Blake Jihad occurs, plunging the Inner Sphere back into galaxy-wide turmoil. Millions die in horrific fashions as entire planets are scourged clean of life, orbital bombardments, chemical bombs, biological weapons, and nuclear warfare run rampant, and things generally go to hell in a handbasket for almost a decade.