(covers information from several alternate timelines)
The Great Houses were a Klingon feudalistic social organization that dominated the Klingon Empire. The twenty-four most powerful Houses were represented on the Klingon High Council. (DIS: "The Vulcan Hello")
By the 24th century, each House was usually led by the eldest male of the ruling family. His wife was the Mistress of the Great House, who typically oversaw the running of the household and approved all marriages into the family. The ruling family was traditionally of noble descent, though this was not always the case by the late 24th century. The Great House also included various properties and holdings, and commanded military forces. (TNG: "Redemption"; DS9: "You Are Cordially Invited")
When the head of a Great House died, either in battle or of natural causes, leadership of the House passed to his heir, usually his eldest son. If the head of the House had been defeated in honorable combat, his wife also had the right to perform the brek'tal ritual and choose his victor as the new head of her House. If the head of the House left no male heir and died under unusual circumstances, the High Council could arrange special dispensation for someone else to rule the House, such as the Mistress. (DS9: "The House of Quark") It was possible for individuals unrelated by blood to join a Great House, by consent of the House's head. (TNG: "The Bonding"; DS9: "Soldiers of the Empire"; see also: R'uustai)
In 2151, T'Pol explained to Klingon captain Vorok that if it were not for Captain Jonathan Archer having found and returned Klaang to the Klingon High Council, "your Houses would be at war with each other," and for that, that Vorok was in Archer's debt. (ENT: "Unexpected")
In 2256, the Empire was dominated by twenty-four Great Houses. T'Kuvma, who led a House not represented on the High Council, attempted to unite all the Houses by pitting the Empire against the Federation. (DIS: "The Vulcan Hello", "Battle at the Binary Stars")
Upon Worf and Kor discovering the Sword of Kahless in 2372, the two argued over who the sword belonged to. Worf believed that it belonged to the Emperor because "It will allow him to unify the Houses against Gowron." (DS9: "The Sword of Kahless")
Years later, when General Martok refused to give Kor a command during the Dominion War, Worf questioned the General's motives, later noting, "There is no feud between our Houses." When Worf brought news of Martok's decision to Kor, Kor reminded Worf, "I know your bloodline. We both come from noble Houses." (DS9: "Once More Unto the Breach")
As later revealed in 2377, according to the Sacred Scrolls followed by Kohlar and his people that sought the kuvah'magh, "You will find me after two warring houses make peace." Kohlar later expanded that interpretation to include the cessation of hostilities between the Klingon Empire and the Federation. (VOY: "Prophecy")
In an alternate 2410, when Alexander Rozhenko, a diplomat by trade, became the leader of the House of Mogh, he thought that he "could single-handedly end the fighting between the Great Houses." He "announced that the House of Mogh would end the feuding, that there would be no more retribution or revenge," yet despite warnings of showing weakness from his father Worf, Alexander found that his "enemies saw my weakness and moved against me," a move that ultimately resulted in the death of Worf on the floor of the Great Council Chamber. (TNG: "Firstborn")
The Klingon Empire was divided between twenty-four Great Houses in the 2250s. (DIS: "The Vulcan Hello") Each of the twenty-four Great Houses in the 2250s held a seat on the High Council. (DIS: "The Vulcan Hello")
The House of Martok was not a powerful noble-born Great House in the 23rd century; due to General Martok's exemplary military career, it rose to political influence in the 24th century. (DS9: "Soldiers of the Empire")
Although some Houses changed their official names depending on who was the current head of the House, others did not (see "Background" below).
Great Houses active in the 22nd century
Great Houses active in the 23rd century
During the 23rd century, political power within the Empire was divided up among twenty-four Great Houses, including:
Lesser houses, not counted among the twenty-four Great Houses, included:
Great Houses active in the 24th century
- House of D'Ghor
- House of Duras (and its mirror universe counterpart House of Duras)
- House of Grilka (temporarily "House of Quark", formerly House of Kozak)
- House of Konjah
- House of Kor
- House of Korath
- House of K'toh-maag
- House of Martok
- House of Mo'Kai
- House of Mogh
- House of Noggra
Ronald D. Moore stated, "We've never explored the hows and whys regarding the naming of Klingon Houses. The House of Mogh reference was probably something that Worf carried on out of respect for his deceased father. This might be the right of a son – to perpetuate a single name for the House instead of supplanting it with his own." (AOL chat, 1997)
The episode "The Bonding" turned out to be the conceptual genesis of Klingon Houses. Recalling his writing of the installment, Ron Moore explained, "I started thinking about [...] Houses, and sort of, you know, the idea of bonding people to a Klingon House [....] The idea of bloodlines and families and sort of this Shakespearian idea of how the Klingon Empire ran – I was starting to, sort of, deal with that in this episode." Moore reckoned, "I think I used the word 'House' in my draft [of 'The Bonding'], even though it's not in the episode." (The Bonding" audio commentary, TNG Season 3 Blu-ray) Neither is the term included in the third revised draft of the installment's script. 
Ron Moore's concept of the conflicting, family-organized Great Houses was inspired by the Dune mythology created by Frank Herbert. In a Klingon-defining memo which Moore sent to Michael Piller at the outset of working on "Sins of the Father", Moore stated, "A Klingon regards the honor of his or her family to be valuable, above all else. The family name can be besmirched by any member of the family, regardless of age or infirmity. A Klingon would sooner kill himself and his closer brother than live with a mark on the name of his ancestral lineage. The family is all, and a member of the family is responsible for the actions of his kin. The oldest son of a Klingon warrior may be called upon to give his life for the actions of his father." The same document also referred to certain families being of importance in the Klingon Empire, the leaders of which comprised the High Council. ("Sins of the Father" audio commentary, TNG Season 3 Blu-ray)
According to an interview with Glenn Hetrick, each of the Great Houses had some of their own unique sub-culture elements in the 23rd century – which faded away in later centuries as their rule became more centralized again. For example, members of the House of Mo'Kai decorated their bodies with ritual scarification patterns, while members of the House of D'Ghor decorated their cranial ridges with extensive jewelry. Members of the House of Kor seemed to be fond of decorating themselves with a stripe of red bodypaint. 
- "The House of Quark"
- "The Way of the Warrior"
- "The Sword of Kahless"
- "Sons of Mogh"
- "Rules of Engagement"
- "Apocalypse Rising"
- "Looking for par'Mach in All the Wrong Places"
- "Soldiers of the Empire"
- "Sons and Daughters"
- "You Are Cordially Invited"
- "Image in the Sand"
- "Shadows and Symbols"
- "Once More Unto the Breach"
- "When It Rains..."
- "Tacking Into the Wind"