Given that the former Seven Kingdoms were really always 8 (II not counted usually, for whatever reason, amongst the Seven (North, Vale, Riverlands, Westerlands, Stormlands, Reach, Dorne), and the Crownlands were created administratively, there are nine constituent regions of Westeros south of the Wall. GRMM makes it clear at the outset (and canonically) who the Great Houses are. The Starks in the North, the Arryns in the Vale, the Tullys in the Riverlands, the Greyjoys on the Iron Islands, the Tyrells in the Reach, Lannisters in the Westerlands, Baratheons in the Stormlands, and the Martells in Dorne with Baratheon of KL's as the Royal house/simultaneously being the default Great House of the Crownlands.
And GRRM gives ample evidence, in addition to outright writing it in places, that other houses outside the "Great" houses are very powerful, to varying degrees. Some of these may be considered "overmighty" bannermen. I love lists and rankings and things of that sort, so I thought it would be fun and a conversation-starter to list the houses of each region, picking the 5 most powerful per region. I would stipulate too a slight difference between most powerful vs. most influential/important. Here's my take on matters:
1. Stark- the Great House, ancient family with deep loyalty from bannermen of region, very strong castle
2. Manderly- controls White Harbor and thus most of the North's commerce, has a small fleet of warships, heavy mounted Calvary. Most knights of any Northern house, and the wealthiest.
3. Bolton- Once Red Kings, ancient house, very strong castle, control large land area, have large amount of soldiers (judging from Roose's actions in the War of 5 Kings and retaking the North post-Red Wedding)
4. Umber- Another ancient line, seems like good number of soldiers available considering sparse population to draw from, known genetically for physical strength and size .
5. Karstark- Good troop numbers and large land area under their control. Power in the North definitely favors those houses on the Eastern side of the continent.
1. Frey- control busiest crossing route on the Green Fork, wealthy and numerous, strong castle. Can field 4,000 men easily, 1,000 of which are knights. Have vassals of their own (Haigh, Erenford, Charlton)
2. Tully- the Great House, control all water traffic at junction of Tumblestone and Red Fork. Good relations seemingly with most houses in region.
3. Mallister- Seagard is a strong castle, and a town grows around it. Formidable warriors historically, usually first defense of Riverlands from ironborn.
4. Blackwood- Putting these two houses in together and by default, as I believe from inference they are stronger than Vance/Whent/Darry/Mooton/Piper/Ryger/Roote, etc.
5. Bracken- see above
The Vale of Arryn:
1. Royce- another surprise here, not a Great House at number one. More by default as Arryn's have very weak leadership right now, house about to pass to some amalgamation of Baelish/Sansa/Harry Hardyng
2. Arryn- the name still carries weight, nearly impregnable fortress in the Eyrie.
3. Grafton- not much info on them militarily, but they control Gulltown and therefore have money.
4. Hunter- these two go in by default, not much is known about their military strength but flip a coin between Hunter/Redfort/Belmore/Melcolm/Templteton/Waynwood/Coldwater/Waxley/Lynderly, etc.
5. Redfort- see above
1. Lannister- Rich, access to gold, Casterly Rock nearly impregenable. Jaime great warrior, Tywin feared leader, Tyrion clever as all get out and Cersei master schemer/evil bitch capable of anything.
2. Lannister- Yup, these guys again. Control, nominally, city and port of Lannisport, can use population to raise troops, theoretically would have the backing of Casterly Rock and vise versa due to blood ties
3. Marbrand- Similar to previous sections, these two houses seem to be close to House Lannister and provide a lot of military support
4. Crakehall- see above
5. Lefford- The castle controls the main entrance to the Westerlands from the east
1. Baratheon of Storm's End- Sort of goes without saying...very powerful house, very strong castle.
2. Swann- Marcher Lords seem the strongest of Baratheon bannermen, and Swann's are an ancient house with a strong castle
3. Dondarrion- Same criteria as above (Caron would make the list aside from them no longer existing as a House, and we can't get confirmation one way or another whether the Selmy's are knights or nobles)
4. Penrose- Putting them here simply because they haven't been overrun by the Golden Company (unlike the Wylde's, Morrigen's, Mertyn's, Estermont's)
5. Staedmon- ditto
The Iron Islands:
1. Greyjoy- Have powerful navy at their disposal, and have essentially been the Kings on the II, as they remain aloof from rest of Westerosi society for the most part
2. Harlaw- Have their own islands/vassals, multiple branches and castles/keeps
3. Goodbrother- Have multiple branches and castles/keeps
4. Botley- Prominent family
5. Drumm- ditto
1. Baratheon/Lannister- Royal family, have the loyalty of Crownlands Houses minus Narrow Sea lords, plus Gold Cloaks and position in Westeros' largest city
2. Baratheon of Dragonstone- Strong island fortress, commands loyalty of Narrow Sea houses (Sunglass, Bar Emmon, Velaryon, Celtigar), seemingly over their loyalty to Iron Throne; naval power
3. Massey- Seem like one of the few legit strong Crownsland houses
4. Staunton- ditto
5. Brune- preeminent house of Crackclaw Point, can fairly safely assume has vassal houses (Cave, Crabb, Hardy, Pyne), multiple branches (Dyre Den and Brownhollow)
1. Hightower- Rulers of Oldtown, ancient and large family
2. Tyrell- Great House, rule large area and population
3. Redwyne- Wealthy and well-protected by island location, strongest private navy in Westeros
4. Tarly- Strong military leadership
5. Toss up between Rowan/Oakheart/Florent/Fossoway's/Costayne/Cuy/Crane/etc.
1. Martell- Great House, two castles (Sunspear, Water Gardens), very loyal bannermen
2. Yronwood- Powerful, ancient, guard the Boneway
3. Fowler- Guards Prince's Pass
4. Wyl- Dornish Marcher Lords
5. Blackmont- Dornish Marcher Lords
What would your list/reasons be?