What are the top 10 most powerful houses (in descending order) as of now?

[Falcon2908]

On 9/3/2016 at 10:45 PM, Chaircat Meow said:

Neither are the Arryns then. All they have is one snotty kid.

There are the Arryns of Gulltown. They are a cadet branch, but Arryns more or less.

[dariopatke]

On 3.9.2016. at 2:55 PM, Chaircat Meow said:

No he doesn't. He has taken 1 or 2 castles in the Stormlands and there is no dornish alliance as of yet.

Griffins Roost, half of Stepstones, Crows Nest, Rain House, Greenstone, Evenfall Hall and

Mistwood and Storms End

are far from 1 or 2 castles.

[Firefae]

1. Tyrell

2. Baelish

3. Martell

4. Greyjoy

5. Lannister

6. Bolton

7. Redwyne

8. Arryn

 

9. Hightower

10. Frey

(I'm excluding Targs here)

[867-5309]

1. Targaryen - Three dragons, 8K Unsullied, three elephants, and thousands of former slaves in training to serve Mhysa.
2. Lannister - Richest family, currently holds the throne.
3. Tyrell - Rich family, can support and feed a large army.
4. Hightower
5. Arryn - Untouched by war.
6. Frey - They dismantled the Starks and ended Robb's rebellion with very little casualty to themselves.  They are rich and very numerous.
7. Bolton - Current ruling house of the North, though they are on shaky ground.
8. Martell
9. Greyjoy
10. Redwyne

*The Harpy - A very secretive, well-funded, evil, terrorists organization dedicated to the vile practice of slavery. Composed of hired mercenaries, sellswords, street thugs, former masters, and slave traders.  True, they are not a "house" in the traditional sense but they are of one mind, one culture.   If we were to include them, I would place them at #4.

[Wolf's Bane]

On 9/3/2016 at 8:35 AM, Chaircat Meow said:

The head of House Targaryen (Dany) has three dragons. Surely that puts her near the top.

That would put her at the top actually.  If we were to limit the choices to the houses currently in Westeros, I would rank them this way.

1. Lannister
2. Tyrell
3. Arryn
4. Frey - Assuming they can call on Riverrun's levies in addition to their own.
5. Greyjoy - I think very little of the Ironfleet will remain after the battle with the slavers.
6. Hightower - they are rich but that doesn't mean they can field a lot of armsmen
7. Martell - They should have more men than the Freys and the Hightowers, but this is assuming any fighting will take place outside of Dorne. 
8. Bolton
9. Aegon/Young Griff
10. Redwyne

[The Lord of the Crossing]

Strictly going by military power and including all known "houses" in the world:

1. Targaryen - Three dragons.  The Unsullied.  Soldiers-in-training.  The company of ex-slaves who support Dany.  Mercenaries.  The Brazen Beasts.
2. Tyrell - The Reach has the population to support a large army and the wealth to finance war.
3. Lannisters - Large standing army.  The City Watch.  Wealth to finance war.
4. Martell
5. Arryn
6. Blackfyre - Ten thousand mercenaries and their war machines.
7. Frey
8. Hightower
9. Greyjoy
10. Manderly

[Endymion I Targaryen]

1. Tyrell
2. Arryn
3. Lannister
4. Martell
5. Greyjoy
6. Bolton
7. Targaryen (Daenerys)
8. Targaryen (Aegon)
9. Hightower
10. Frey

My choice was influenced by the Winds of Winter sample chapters.

[thi4f]

In military terms, it could go like this:

1. Tyrell. They started with the largest army and still have at least 70% of previous potential. Maybe little less, it depends on what's going on at Dragonstone and Storm's End.
2. Arryn. All of their power is intact, although leadership is questionable.
3. Martell. Similar situation, I think this top 3 is set in stone at this moment.
4. Greyjoy. Doesn't Victarion command some 90 ships himself? They had losses in the North, but more than a half is still ready to fight, plus Euron reinforced their fleet.
5. Hightower. Arguably the strongest second tier House in Westeros, I wouldn't be shocked if they field fifteen thousand men at the moment.
6. Lannister, including Baratheon of King's Landing. They are banged up pretty badly after Wot5K, but Westerlands had great manpower in the beginning (some 40k).
7. Targaryen (Aegon). I don't remember how many mercenaries already landed in Westeros, but if we count all his forces, total number could be north of 10.000.
8. Bolton. Not that strong by themselves, but I include Frey, Karstark, Umber and other northern houses. Somewhere between 5 and 10 thousand men.
9. Manderly. Don't remember the estimates, but I think six thousand is safe bet.
10. Baratheon of Dragonstone. Stannis still commands some five thousand men, although it resembles Hannibal's army: some knights from Stormlands, Crownlands, Narrow Sea, mountain clans, northern houses... not cohesive and hard to use to its full potential.