Man rules now where They ruled once; They shall soon rule where man rules now. After summer is winter, and after winter summer. They wait patient and potent, for here shall They reign again. — The Necronomicon
In the beginning, when the world was first formed out of dust and ice, before mankind came to dominance, the world was ruled by dark forces, evils beyond imagination, ancient tyrants. Or at least that's what some horror and fantasy stories want you to believe, that before man arrived (and even sometimes after) there were creatures that ruled this world that are now gone.
Most often, this is important to the Back Story of a series, giving writers room to introduce remnants of those old evils sealed in a can. Sometimes The Dark Times become The Time of Myths and then lead to Götterdämmerung. Alternatively, the creatures that populated The Dark Times are merely waiting Beneath the Earth until they regain their strength.
In One Piece, the past has been completely censored by the World Government. The ability to read the hieroglyphs that the ancients wrote is enough to make the World Government use the most powerful attack known to mankind to completely wipe an island off the map.
Although considering how ruthlessly amoral the World Government is on so many levels, it's anybody's guess if these times were any worse than present times.
An alternate fan theory is that the World Government IS the terrible enemy spoken of in the ancient texts and which potentially world-destroying weapons were created to fight.
Devilman's backstory involves demons returning after having been dormant since around the ice age.
The world of Naruto was besieged by the near-almighty Ten-Tailed Beast centuries ago, until it was sealed and imprisoned by The Sage of Six Paths.
Star Wars frequently referred to the war between the Jedi and Sith, which lead to the dominance of the Jedi, and the threat of the prequel trilogy is solely the return of the Sith.
The gap between Episode III and Episode IV are referred to as "The Dark Times", in-universe. Specifically by Obi-Wan in A New Hope when giving Luke the short version of the Jedi Purge and his father's death.
In Thor: The Dark World, the Dark World of the title is the home of the Dark Elves, a race from before the current universe who wish to return all that exists to this state of non-existence.
Midkemia of The Riftwar Cycle was ruled for an untold amount of time by the Valheru, beings who arose long before the coming of the younger races and even the gods. They were enormously powerful and, at the time, not so much consciously evil as totally amoral. They lived out their time by sporadically killing one another, enslaving entire races, and periodically riding out to slaughter and sack entire worlds. Their conflict with the newly created gods and their expulsion after their defeat is a vital backstory point.
Middle-Earth has cycled through various dark times when Morgoth and/or Sauron were the dominant forces in the world (perhaps the most notable being when Melkor/Morgoth ruled the all of the world except for Valinor completely unchallenged- it was only the coming of the elves that inspired the Valar to act against him). The plot of The Lord of the Rings basically consists of Sauron trying to start up new dark times.
The Cal Leandros series includes as part of its distant past a time when the world was ruled by various monsters like the Auphe.
A Star Trek crossover event, Invasion! introduced the Furies, a coalition of species that once ruled Federation-and-neighboring space. All the local cultures remember at least one Fury species as their "demons". The Furies were overthrown by the Unclean, who require three things from other species: power cores, DNA, and BRAINS! Unfortunately, each novel's author hada slightly different take on the Furies.
A Song of Ice and Fire has the Long Night, occurring 8000+ years before the main storyline begins, with the emergence of the Others and their legions of wights.
This idea actually evolved through Buffy the Vampire Slayer and Angel - in early Buffy, the Old Ones were implied to be merely waiting for a chance to come back and continue their reign, but by the time we came to late Angel and actually met one (Illyria), they were shown to have mostly killed one another and now are sealed away in specially-designed sarcophagi.
There are "the Dark Times" of Gallifreyan history when Gallifrey was ruled by the Pythia before she was overthrown by the triumvirate of Rassilon, Omega, and the Other.
Many of the races on Babylon 5 had legends concerning the last war with the Shadows 1,000 years ago: most of the Narn telepaths followed G'Quan to war and never returned; the Minbari almost lost the war until the timely arrival of Valen and a replacement base of operations; the Markab spoke of the "great darkness" defeated long ago several episodes before they were conveniently wiped out by a plague.
the Norse have the frost-giants ruling over a frigid, misty world in the time before Odin and his brothers slew Ymir.
In Greek Mythology, there are the first generation of Gaia's offspring- the titans and the altogether stranger Giants, Hekatonkhires, and Cyclopes.
Although this varies depending on the source; some claim that time was a Golden Age (this is where the term originated, in fact).
Irish mythology has the island originally inhabited by the monstrous Fomorians, before they're ousted during an extremely complicated series of invasions.
In The Bible, it's implied that during the time when the Earth was formless in the first chapter of Genesis, Satan's Rebellion was in progress. While Adam and Eve were initially spared from experiencing this conflict, it all went to pot when they were tempted to eat from the Tree of the Knowledge of Good and Evil, kicking off a period when humans became increasingly more wicked and started producing giant offspring with angels. Things got so bad that God had to destroy the old world in The Great Flood minus everyone and everything in the Ark.
Also, according to the RNA World hypothesis, before DNA based life appeared, the world was once dominated by things which were basically viruses, although modern viruses may not have any connection to them.
Prior to the emergence and spread of cyanobacteria, Earth's atmosphere was anaerobic, and deadly to nearly everything alive today. Earlier still, it was so hot that the surface was molten, and vaporized rock was a component of the air.
And, well, the nature of whatever space the universe would eventually occupy right before the Big Bang is totally unknown to us.
In the Continuum RPG, the time before 14,000 BC was/is ruled by the civilization of Antedesertium, whose Narcissistic experiments and attacks on the timestream led to their Scorpion Kings becoming Eldritch Abominations, before finally destroying their civilization, triggering more or less a millenium of temporal chaos that led to the creation of the Sahara Desert.
Warhammer 40,000 has several Dark Times: the aftermath of "The War in Heaven" stands out when all life was enslaved under the rule of the C'tan, until a plague of Eldritch Abominations killed 99% of all living things.
By most series' standards, Warhammer 40k is entirely made up of Dark Times.
40k subverts this trope by having the present be the Dark Times with the past for the Imperium and the Eldar being depicted as glorious golden ages undone by their own pride. Since then it just keeps getting worse.
Warhammer Fantasy had a fairly brief Dark Times, the period between the Old Ones' fall unleashing the Chaos gods, and the High elves succeeding in mostly closing the Warp Gate that let Chaos in. Of course, everything still sucks, but Chaos doesn't dominate the majority of the world anymore.
Microscope: Being a game of emerging history, this comes up a lot. Every Period and Event has a Dark or Light cast to it.
BIONICLE had its own Dark Time, and it was called just that, but it wasn't ancient. That is, it wasn't for most people, save for the tribes on the Mata Nui island, whose memories had been wiped. The era started with the Great Cataclysm 1000 years ago and ended directly before the main plot began — but it only lasted for 999 years on the island of Mata Nui, because the Big Bad agreed to give the islanders one spare year to build their villages that he later wanted to besiege. The rest of the Universe wasn't as lucky.
Then in the second game, turns out they were Not Quite Dead after all...
World of Warcraft: The lore behind Azeroth is that there was once a time when the Old Gods ruled and had chaotic elemental lords as their lieutenants to strike terror in the hearts of many. The titans came and put a boot in their behinds, killed one or two of them and put the rest in solitary confinement.
It should be noted that the Titans are pretty much Physical Gods / Precursors in the Warcraft Universe. They created most of the life on Azeroth, and where PISSED when the Old Gods started screwing with their creations, namely the Curse of Flesh which made all of their metallic creatures "Squishy". In fact, this scared them so badly, they left Azeroth with a self-destruct mechanism on the off chance their influence spreads. Better to lose one world then all of them.
The backstory of RWBY is about how mankind was nearly killed by evil creatures called Grimm, whom they managed to drive back by harnessing an energy source called Dust and channeling their Auras for fight capacity. The inhabitants of that world are at least smart enough to prepare for the Grimm's inevitable return.
What happened, deep in the hidden eras before history began, that could affect the entire human race so evenly as to give the entire species a deep, instinctual, and lasting fear of pale beings with dark, sunken eyes, razor sharp teeth, and elongated faces?
In "Hearth's Warming Eve", the ponies of the past nearly faced extinction as the Windigoes fed on their hatred to turn the entire landscape into a frozen wasteland. What makes this example worse than the others is that the ponies ultimately only had themselves to blame for the situation instead of an Evil Overlord.
In The Legend of Korra midseason two-parter "Beginnings", before the time of the first Avatar, the physical world was overrun by spirits, many of them hostile to humans, forcing them to live in cities on lion turtles. Although the lion turtles were able to give their citizens the power of element bending, it wasn't much help against the power of the spirits, especially when corrupted by Vaatu. These times came to an end when the first Avatar, Wan, decided to let the vast majority of spirits return to their place of origin, the spirit world, and let them be unable to return by sealing the portals between the physical and spirit worlds.