House Targaryen had arguably been the most influential in Westeros for centuries prior to Robert’s Rebellion. But them aside, which other house has also played a huge role in the shaping of Westeros? And why?
House Stark. They’re one of the oldest houses by thousands of years and ruled the north for most of that. It was a Stark after all that started the events leading to the events of the books.
Hightower. Money, location, and have been around even before Westeros. Married into Targs constantly, have access to the faith and the Citadel. Definitely some of the most influential in my opinion/formational
House Arryn, at least in recent history.
Jon Arryn was a major influence and father figure for both Ned and Robert, was the first lord to call the banners against the Mad King, and then was Robert’s Hand.
Can’t think of anyone else who influenced events more than that prior to Robert’s Rebellion.
House Arryn is a good one because I think it also stands out as among the first and most prominent of the Andal invasion, which was a defining moment. The Andal invasion changed the culture of Westeros and splits up the landmass. It’s also a place that during the modern era has a mix of First Men and Andal people living there, showing again the Andal influence and shift of power.
I’d also then put House Martell as another one of the most influential houses, considering how much the Rhoynar migration changed the culture of Dorne and the politics of Westeros.
I’d say House Hoare was extremely influential. They ruled the Iron Islands from the Andal Invasion until Aegon’s Conquest apart from one brief period of occupation, as such they were in charge for thousands of years, and likely synonymous with the Ironborn and Reavers.