Old Ones, a term popularized by H.P. Lovecraft and the Cthulhu Mythos, is a type of entity used in fantasy games for the culture that was first on the scene in creation, before the limits of recorded history in the current setting of the game. This culture is always described as awesomely powerful, responsible for shaping entire landscapes, sinking continents beneath the waves, or giving birth to new races An important feature of a race of Old Ones is they aren't around anymore -- or if they are, it's in some degenerate form (reduced to stone-age beasts, or secluded colony hiding from the world, or one sleeping god-like individual).
"Precursors" is the sci-fi version of the term, but doesn't carry as much inherent connotation of malevolence, though it's still very possible (think Pacific Rim…or halo, if you know).
Call of Cthulhu
There were many "Old Ones" in the Cthulhu Mythos, and thus the Call of Cthulhu RPG. It's most commonly used to refer to one of the following two:
The Great Old Ones were alien beings of colossal size, and not exactly normal physics. All the Great Old Ones have been slain or imprisoned by Elder Gods, some entombed in planets like Earth. Some theorize that the Great Old Ones are imprisoned for the crime of practicing blasphemous black magic, and the Great Old Ones are just waiting to break out and avenge themselves. Others theorize the Great Old Ones submitted willingly to imprisonment, as a way to sleep away the aeons "until the stars are right" and they can resume their awful practices.
The race of Old Ones (or Elder Things) were extraterrestrials that traveled between the stars, and set up a colony on primordial Earth. They built a city on the southern polar continent and experimented with the local biology to create a servant caste. Their discards were tossed to the other continents (
the Cambrian Explosion? The Cambrian Explosion pre-dated life on land.The Elder Things, when they spanned the globe, set up cities both underwater and on land, so, entirely possible.) and settled on their ideal lowest-class citizens: the Shoggoths, amorphous blobs of eyes and toothy mouths. The Shoggoths formed a rebellion and overthrew their masters, killing almost every single one because the Elder Things held them in thrall with hypnosis for over 2 billion years.
In the time before time the Primordials wrenched a world from the bleeding edge of chaos and peopled it with gods, men, Dragon Kings, the People of Adamant, the Lintha, and more.
Then the gods and humans joined forces and made war on the Primordials, killing many of their number and trapping the rest in the body of their king, which had been turned inside-out, and cast them out beyond the confines of this world.
In the brass-and-bone depths of the Demon City, their demonic progeny turn wretched eyes our way, ever watchful for a crack to appear in their prison. Meanwhile, the slain titans have formed a dark mirror of our world, save that at its center is a twisted labyrinth of their congealed nightmares, and at the center of *that* is the concept of oblivion made manifest, above which hang their dead-but-dreaming tomb-bodies.
Long long time ago, a lizardman type race had a huge empire that enslaved all the "warmbloods." It was probably the Sarrukh, mentioned in the Serpent Kingdoms splatbook. They're supposed to be extinct now, but it would make a decent BBEG. The Story of the first Neverwinter Nights video game explored this but made it all very confusing and disappointing.
The old-ones in Traveller are called the "Ancients," and their sites can be found in any random place. The architecture can vary wildly, from habitrail tunnels hermetically sealed and protected from a benign environment, to hollowed-out crystals hundreds of feet high with no ladders or stairs. None of the sites have any documentation, many of them expect visitors to be able to fly or use telepathy, and all of them are empty and inert... except maybe whatever one your adventurers carelessly step into . Each Ancient site predates the literacy of every civilization, and doesn't seem to have anything in common with other Ancient sites other than being built for inhabitants that are 1-2 metres tall. Ancient sites make for good dungeon romps in what is otherwise a hard sci-fi campaign about making mortgage payments on your spaceship.
The Ancients also explain why there's so many humans in space. The first great human empire was the Vilani empire, built by the humans that first discovered faster-than-light travel. They were pretty surprised to find out there were other aliens around; even more surprised when they encountered another FTL space-faring empire of humans called the 'Zhodani.' Scientists concluded sure that the two-arms & two-legs body shape was just naturally better for most environments, and stopped being surprised that everyone was "humanoid" shaped. This all went to shit when a third race of humans showed up with FTL drive, calling themselves the 'men of Sol' ("Solomani" in Vilani), and it turned out that they came from a world where the entire ecosystem was integrated, not evolving in parallel like everywhere else. Vilani scientists were certain this was a sign that the Solomani were an engineered race of humans made by the Ancients, what with everything fitting together like clockwork. Instead, they discovered the opposite: the undeniable conclusion that Zhodani humans, Vilani humans, and all the other humans from minor races were "seeded" from Sol-3 and transplanted to every other world by the Ancients. Even the biology of the lupine Vargyr major race were seeded from this 'Earth' world. This gives the Solomani a superiority complex that makes them pretty insufferable to be around.
This continues the trend of hard sci-fi ignoring 'hard biology'.
Both Warhammer Fantasy Battle and Warhammer 40,000 feature major background events caused by Old Ones. There is some debate about whether they are both the same or different. In 40k: they were reptilian; battled against the Necrontyr and C'tan; used genetic engineering to create the Eldar, Humanity's ancestors (kinda, but not really since human ancestors didn’t exist back then...), and the Orks; and created the Webway. We also have them to thank for the existence of the Chaos Gods since before the War in Heaven, the Warp was known to have been a far more placid realm. Boy did that change. In short, for all intents and purposes, this effectively means that the Old Ones, Necrons, and C'tan are the progenitors of the Chaos Gods. At best, the Old Ones are equally responsible for this outcome as the other two. Though, given their penchant for warp dabbling in contrast to the absolute non-existence of the same from the Necrons and C'tan, it's perhaps more likely that the Old Ones hold a higher percentage of the blame. If nothing else, this all probably puts the Old Ones at the top of the list of architects of the greatest ever instances of Not As Planned. That's something.
In Warhammer Fantasy, they arrived to Warhammer World from space, seeing (probably) its potential in colonisation or maybe they wanted to use it as a part of their plan to stop Chaos. They, however, were pissed off by planet's climate and used their and Slann magic to literally pull the world out of Ice Age and reshape the continents when they needed it. After that they started creation (or genetical modification, it's not exactly known) of different races to battle Chaos, although they failed every time. Every major race (with exception of Orcs & Goblins and Chaos-related species like Skaven) were created by them, and even more were genocided by Old Ones' loyal servants, Lizardmen. And then, when Old Ones desperately tried to fix their latest failure, Chaos Gates collapsed, Daemons were released and they mysteriously disappeared, leaving only plaques with some of their instructions.
The World of Warcraft is decorated with sci-fi elements in its origin story, so it has both Precursors and Old Ones.
A race of godlike beings called Titans do the classic Precursor thing of "seed viable worlds with new life, then get bored and wander off thousands of years before any protagonists are born." They even have the cliche of one Precursor turning rebellious teenager, writing bad poetry and trying to destroy all the new life that the rest of the family worked so hard to build. The minions of the emo Titan are the demons & devils you usually see in fantasy games.
The viable world that is the setting for the Warcraft stories is extra-special, because it has four or so creatures known as the "Old Gods" that are nasty moustache-twirling villain gods with HP Lovecraft inspired names. The Titan Precursors tried to evict them so the world would be better for playing SimEarth with, but couldn't, so just imprisoned them under the planet's crust. Once the Titans left, the Old Gods fucked with the seeded life to corrupt it, even fucked with the dragons the titans created as janitors for the planet, and to fuck with everyone's heads to create cultists and generally make everyone miserable.