At its core, George R.R. Martin's A Song of Ice and Fire, and its TV adaptation, Game of Thrones, tell the story of the nine noble houses of Westeros. While each great house is revered throughout Westeros in-universe, some have made far more of an impact on audiences than others. Even the most casual Game of Thrones fan will know the names Stark, Lannister, and Targaryen, but several of the other great houses come across as somewhat deeper cuts.
The nine great houses of Westeros are House Stark of Winterfell, House Lannister of Casterly Rock, House Baratheon of Storm's End, House Greyjoy of Pyke, House Arryn of the Eyrie, House Martell of Sunspear, House Tully of Riverrun, House Tyrell of Highgarden, and House Targaryen, who, up until Robert's Rebellion, ruled the Seven Kingdoms from King's Landing. Each of these houses represents an important region of Westeros.
While not all of the great houses receive the same amount of focus in Game of Thrones, Martin has fully developed all nine of them, resulting in rich lore for even the least important among them. In fact, the least prominent great house in Game of Thrones subtly takes center stage in one of the franchise's biggest spin-offs.

The least important great house in Game of Thrones
Every episode of Game of Thrones opens with an iconic title sequence, in which viewers watch the map of Westeros unfold, with extra focus on the locations that will be relevant in each episode. Additionally, as the main cast's names appear, they are accompanied by the sigil of their character's house, be it one of the nine most prominent in Westeros, a minor house, or another symbol associated with more lowborn characters.
Seven of the nine noble houses are represented by these main cast members. House Stark takes up a good portion of the cast.
House Lannister has three of the series' main characters, Tyrion (Peter Dinklage), Cersei (Lena Headey), and Jaime (Nikolaj Coster-Waldau), as well as their patriarch, Tywin (Charles Dance), and House Baratheon is represented by King Robert (Mark Addy), as well as his wife's sons who are falsely regarded as his children, Joffrey (Jack Gleason) and Tommen (Dean-Charles Chapman), his bastard son Gendry (Joe Dempsie), and his brother Stannis (Stephen Dillane), whose Baratheon sigil is slightly different than the rest of his family's to highlight his connection to the red woman, Melisandre (Carice van Houten).
House Targaryen, of course, has Daenerys (Emilia Clarke) and, briefly, her brother Viserys (Harry Lloyd). Houses Greyjoy and Tyrell have one main cast member each, Theon (Alfie Allen) and Margaery (Natalie Dormer), respectively, despite a handful of other members of those houses playing prominent roles throughout the series. Finally, while House Tully's trout sigil never appears in the opening credits, a key character, Catelyn Stark (Michelle Fairley), still represents the Lords of the Riverlands, although her name appears next to the Stark's direwolf, her husband's sigil, instead.
As such, the only two great houses without any cast members in the opening credits are Houses Martell and Arryn. However, given the prominent role Prince Oberyn Martell (Pedro Pascal) plays in season 4, despite being credited as a guest star, and that in seasons 5, 6, and 7, House Martell ally Ellaria Sand (Indira Varma) receives main cast billing, not to mention the numerous Martell point-of-view characters from A Song of Ice and Fire, it's safe to say that House Martell has received its fair share of focus in the series, leaving House Arryn as the least represented of the nine great houses.
House Arryn's underrepresentation likely stems from the fact that the death of their patriarch, Jon Arryn (John Standing), kicks off the events of the series, meaning he plays no active role in the events that follow. While his wife Lysa (Kate Dickie) and son Robin (Lino Facioli) occasionally appear, their roles are much smaller than the rest of the nobles, especially since, shortly after arriving in the Eyrie, Littlefinger (Aidan Gillen) murders Lysa and effectively takes control of the Vale himself.

House Arryn's role in House of the Dragon
As the title would suggest, House of the Dragon, the first major spin-off of Game of Thrones to be produced by HBO, focuses primarily on House Targaryen. Most of the series' main characters, including Viserys (Paddy Considine), Daemon (Matt Smith), and Rhaenyra (Emma D'Arcy), are Targaryens.
However, the series' first episode, "The Heirs of the Dragon," features a hugely important character who, sadly, dies right away: Aemma Arryn (Siân Brooke). Aemma, the wife of King Viserys, dies in childbirth along with her son, leaving her husband's line of succession muddled, since their only surviving child, Rhaenyra, is female.
As such, Rhaenyra, arguably the most important character in all of House of the Dragon, is a member of House Arryn. While her father is a Targaryen, and she bears his last name, Rhaenyra, unlike many other Targaryens who are purely inbred, has the blood of two great houses. Additionally, this makes Rhaenyra's children, including Jacaerys (Harry Collett), Lucerys (Eliot Grihault), and young Joffrey (Oscar Eskinazi), all major characters, members of House Arryn as well.
Season 2 of House of the Dragon also introduces another fairly important member of the house, Jeyne Arryn (Amanda Collin), who pledges the support of the Vale to the Blacks in exchange for the protection of a dragonrider, adding another Arryn character to the list.
Although she is easily identified as a Targaryen, Rhaenyra is also the single most prominent member of House Arryn in the entire franchise, subtly giving the great house more focus than the original series ever did.
