Orcs are The Horde by nature and will form bandit gangs on their own, but Sauron is able to beat them into a more disciplined army. His Orcs are "officially" known by numbers rather than names, have rules for processing prisoners found sneaking into Mordor, and are forced to work along with Mordor's various client states as part of The Empire.
The Easterling nations, especially the Balchoth and the Wainriders.
The Reynard Cycle: One of the many reasons that Vulp Vora is so dangerous is due to it being inhabited by the Chimera, who breed to the point where they must expel a portion of their population in this fashion. Their "neighbors" the Calvarians build their fortresses near choke points in order to defend themselves against these.
The series also has the Dothraki, generally well done Expys of the Mongols.
The nomad tribes in the Warworld series (part of the CoDominium setting) fill this role towards the settled farming societies. The HaBandari and the Saurons manipulate the nomads strategically, driving them back and forth across the steppe into each others' territories. In Blood Vengance when some of the allied tribes slip past the Sauron Citadel into the undefended Shangri-La Valley, one of the Bandari compares them to packs of ravenous wolves and the valley's unarmed farmers as sheep.
The Mongols in the Conqueror books, a rare case of The Horde being the protagonists. The Tartars in the first book might also qualify, making it a case of Horde vs Horde.
The Kargs of the Earthsea Trilogy come off as this, particularly in A Wizard of Earthsea, where they're essentially Vikings. They get some Character Development in the next book, The Tombs of Atuan, but it's pretty clear that most of Earthsea considers them to be exactly this trope.
The Shas-ga in Mikhail Akhmanov's The Sword above the Abyss are nomadic barbarians from planet Ravana (AKA Inferno), who roam the barren steppes north of an impassable mountain range on the Western continent. While normally divided into tribal groups called Hearths, they are now united by a powerful leader called Grey Trumpeter (a title, not a name, kind of like Genghis Khan), who has managed to find a passage through the mountains to the more temperate southern lands. The Shas-ga are cannibals and often kill their own women and children for food and as sacrifices to their gods. Their warriors ride on massive ox-like beasts with a nasty temper. Now that they have crossed the mountains, their enormous horde (about 30,000 warriors, which is big number on Ravana, whose population is small) threatens to wipe out the much more civilized cultures on the southern part of the continent, unless the disparate Kjoll barons, the eastern trade towns, and even the southern barbarians join together to meet this threat.
In New Jedi Order, the Yuuzhan Vong start out as a space-faring version of The Horde. After taking Coruscant midway through the series and becoming the galaxy's dominant political power, they morph into The Empire.
Nicely Averted in many of David Drake's books - a student of Byzantine history he takes pains to explain that chroniclers ALWAYS wrote up defeats as being at the hands of INSANE numbers of enemies rather than the truth: the horde were always highly skilled and highly mobile combat pragmatists who outfought the clumsier "career military" of civilized nations.
The first is the Canim, nine-foot wolfmen who are a Proud Warrior Race and occasionally launch raiding parties at Alera from across the sea.
However, a better example is the Marat, who live on the neighboring continent and occasionally launch massive hordes through the neighboring isthmus. It is one of these raids that leads to the start of the series fifteen years prior, and an actual horde attack occurs at the climax of the first book.
Both are deconstructions of the trope, though. They have sympathetic motives and are willing to meet the protagonists halfway, eventually even allying to take on a much bigger horde:
The Vord, a shapechanging, zerg-shout-out army that sweeps most of the continent.
Trollocs in the Wheel of Time are bio-engineered horrors built by the forces of the Dark to fight the Light in the last cataclysmic war between light and dark in the world's cyclic history.
Harry Harrison's Deathworld 3 (originally published as The Horse Barbarians) has Jason invite some of the Pyrrans to help colonize the mineral-rich planet Felicity, a Lost Colony. Unfortunately, the mining efforts are being thwarted by Mongol-like tribes of nomads who roam the steppes of the plateau covering a large chunk of the planet's only continent. Due to their beliefs, any permanent structure is deemed as evil and must be destroyed along with those who have perpetraed this deed. Naturally, this goes against any plans to mine resources on Felicity. The normally warring tribes have banded together under the banner of Temujin, who has vowed to keep their traditions and destroy the otherworlders who violate their rules. Jason infiltrates the horde as a Wandering Minstrel from a tribe that has yet to join and manages to get close to Temujin. However, the chief figures out that Jason is lying and throws him into a pit. Jason survives and finds out that the fertile lowlands are home to a Medieval agrarian culture. He comes back as a "spirit" to Temujin and leads him on a great crusade to destroy the lowland offenders and even teaches the nomads some of their technology, such as gunpowder. At the end, the fate of the nomads directly mirrors that of the Real Life Mongols. After conquering the lowlands, they start enjoying the luxuries of sedentary life and abandon their traditions. Temujin realizes this but can't undo what was done. The plateau is abandoned, and the Pyrrans are free to mine it.
The Lost Regiment series has the Tugars, 10-foot-tall hairy man-eating Mongol Expys, who are engaged in an unending journey around their world (which lacks oceans), feasting on the various human peoples who have been brought there by a Negative Space Wedgie before moving on, expecting the population of the "cattle" to replenish before their next circle. They ride vicious horse-like beasts (with two rows of sharp teeth) and demand that the human nations pick a certain number of their people to sacrifice. Later books reveal other hordes (the Merki and the Bantag) making the same circle around the world but at different latitudes. They belong to the same species but are warring with one another over territory and food. The Bantag also have 20th-century-level technology.
Somewhat subverted in Eberron, where two different Hordes have settled down and are trying to become The Empire, with varying degrees of success. One is actually a former Empire trying to get back on its feet after a demonic invasion that, in a major departure from expectation, they were in no way responsible for, and went a long ways in preventing the recurrence of.
GURPS Mass Combat is designed to simulate hordes of fighters on both sides. The first example given in 4th edition rules is ninjas that jump off dragons and float to the ground on giant kites.
The Sub-Demon race known as Brodkil often carry this role in Rifts North America, but there are also plenty of Human bandits such as the Pecos Empire. The Southern half of South America is commonly beset by a race known as the Larhold, the Japanese Oni have made a comeback, and the Hourne Pirates ensure that the seas aren't safe, either. But in Soviet Russia, the Hordes civilize you! The ten Warlords and their armies of Cyborg soldiers hold most of the power.
The Vargr in Traveller are stereotyped as this; though they're capable of building starships that requires a great deal of organization and can form city-states and nations, they're still prone to far more instability then humans.
There are, however, factions antagonistic to both the Horde and the Alliance that fit the trope much better. The Undead Scourge, the aforementioned Burning Legion, the minions of the Old Gods, and several offshoots of the orcish Horde who cling to warmongering for warmongering's sake: Rend Blackhand's Dark Horde, the Fel Horde on Outland who still bear the curse of demonic blood, Garrosh Hellscream's attempt to ban the 'lesser races' and create an orc-only True Horde, and, as of Warlords of Draenor, also the Steam PunkIron Horde that comes invading Azeroth from a parallel timeline.
In the new Mists of Pandaria expansion, there is a group of anthropomorphic yaks, known as the Yaungol, who you can probably tell are based off the Mongols. They fight much like them as well, as a ruthless horde.
The Minion Army of the Overlord games, commanded by You.
Gray Mann's robots in Team Fortress 2 spawn in large swarms in the Mann Vs Machine game mode. Taken Up to Eleven (or should we say, Up To 666) with the Ghost Town Halloween Event, where the aptly named Wave 666 consists of 911 robots and 9 tanks, and additional Spies and Snipers which spawn for as long as you play, potentially bringing the total to well over a thousand.
The Darkspawn in Dragon Age come swooping down on the human kingdoms every few centuries. And swooping is bad.
The Sha'ahoul in Siege of Avalon, a nomadic race of human/orc hybrids who believe that any permanent structure or farming is harming the world of Eurale and must be destroyed. Imagine their surprise when one fine day they stumble on the seven kingdoms, who do all that and more. They gather a massive horde and attack. The kingdoms' only hope is the fortress of Avalon, the only thing that stands in the way of the Sha'ahoul. The horde's leader Mithras is determined to raze the offending structure and starts the titular siege.
Though Caesar's Legion of Fallout: New Vegas styles itself as a post-apocalypticRoman Empire, Caesar will privately admit that his forces are closer to the Gallic barbarians than true Legionnaires. Hence his interest in the titular city, a New Rome that will provide a proper capital for his empire.
Drowtales has the Nidraa'chal, who actively employed demons to possess commoners while fighting the Sharen. There's also the Black Sun, a group of tribes that subsist by raiding cities and settlements, and operate similarly to Mongol hordes in the sense that they are heavily decentralized and will absorb captured enemies into their ranks, and several Black Sun tribes will band together for particularly tough fights.
Troll civilisation in Homestuck is like this - all adult trolls, all of whom are conscripted into the military, have been banished from the troll homeworld in order to conquer planets for their Empress, which they do so with brutal efficiency. The troll homeworld is used exclusively for raising baby trolls to adulthood, and the children are encouraged to kill and deceive one another to survive. The kids' antics look pretty dark to us viewers, until we discover through Mindfang's diaries what kind of horrible lives adult trolls are expected to live, casting their actions in an altogether more innocent light.
In The Gamers Alliance, four demon hordes, led by their respective dukes and duchesses, settle into Yamato after the Cataclysm and scheme against one another.
The Drifalcand in Guts and Sass: An Anti-Epic are an unorganized, pantheistic, (heterosexually) orgiastic invading horde who conceive of conquer as an end, not a means. They're kind of like a human natural disaster: they destroy, they move on.
Truth In Television
Though the victims of a real world raiding culture will perceive their attackers as this, it should go without saying that people like the Vikings or Mongols were more complicated than The Horde.
The Mongols were actually more organized and disciplined than popular portrayals tend to show them to be, part of why they won so many battles. Not that it was any comfort to their enemies, since they had a very mobile army and looked larger than they were because several reports came into their enemies headquarters from different places at the same time. Each warrior also had two or three horses so that he could switch between them for long journeys and not exhaust them, making thee army look much larger. And once they were done conquering, the Mongols ended up one of the world's largest empires.
The word "horde" comes from Mongolian ordo/orda/ordu/ordon, and originally referred to a tent or campsite; it became associated with the modern connotations of "horde" thanks to the Mongol armies making frequent use of mobile camps during campaigns.
The Vikings of course did not spend all of their time a-viking, and were capable of living as peaceful a home life as anyone else in medieval Europe. It should also be noted that in some cases the Vikings had better hygiene than the people they were raiding. The Vikings, in fact, bore ultimate responsibility for bringing Europe into the modern age; they settled all around the Continent and on most islands, and their advances in seafaring ultimately connected Europe through trade. And as a matter of fact, the most commonly accepted etymology for the word "viking" is that it originally meant a short trip and became a euphemism for a (typically seaborne) raid. A Viking, to the Scandinavians of the "Viking Age", was therefore basically a raider of any ethnicity (one famous band of Vikings in the sagas, the Jomsvikings, was based in what is now Northern Germany), whereas non-raiding Scandinavians wouldn't have been referred to as Vikings.
Common perceptions on the infamous /b/ seem to veer into this territory, particularly when the Wretched Hive shuts down.
Any invading army looks like the Horde if you are in the way.