In A Clash of Kings, there are many different factions competing for control of Westeros in the War of the Five Kings:
How large was each of these armies?
I would say:
Renly > Tywin > Robb > Greyjoy > Stannis.
I seem to recall some numbers being mentioned, such as Renly having 100,000, and Stannis 2,000, but the exact numbers are not really a good measure of the strength of the army. It is the quality of the men, their leader, their position etc. Like when Robb crushed Stafford Lannister's army at Oxcross, they had a lot of men, but they were raw recruits with a poor leader. Or when Ramsay's 700 riders used surprise to crush Rodrik Cassel's 2,000+.
Tywin Lannister has a large army of Westermen, probably of comparable size of that of Robb's army of northerners. Tywin is a shrewd and experienced leader. And he is probably one of the most feared lords in Westeros, because of his cruelty towards his enemies. He extinguished the houses Tarbeck and Reyne for challenging his leadership as lord of the Westerlands. Which means he killed them all, which is more horrible than it sounds. He also killed the Targaryen children during Robert's rebellion.
Robb Stark has all the north and most of the riverlands, which is a sizeable army. Robb himself is inexperienced, though he won all of his battles. Robb has the Blackfish Brynden Tully on his side, who is a formidable leader and strategist.
Renly Baratheon's leadership qualities were never really mentioned. He had, as far as I know, never lead men in battle before. But he did have the notorious Lord Randyll Tarly on his side, who is often mentioned as the best battle commander of them all. Renly has the support of house Tyrell, who has one of the largest armies in Westeros, reportedly around 100,000 strong.
Balon Greyjoy has his ironmen, whose main strength is their fleet. On land, they would probably be quite insignificant compared to other armies, but on the sea, they are one of two major forces: the Redwyne fleet and the ironmen.
Stannis Baratheon, the outsider, the forever awkward man of iron (according to the Night's Watch smith Donal Noye), has the smallest army, ever growing smaller (disregarding the men he took from Renly after their meeting at Storm's End). He is feared, though, because he is relentless, just and an experienced battle commander. His core army consists of the men from his wife's house: House Florent. He is the rightful lord of the Stormlands, with Storm's End as his main seat, but Robert gave Storm's End to Renly, and gave Stannis Dragonstone (which previously was a Targaryen seat, commonly held by the heir apparent). And the lords of the Stormlands chose to follow Renly instead. The lords of the islands around Dragonstone follow Stannis, though they do not have a lot of men.
At a guess, I would put the numbers at
Renly 100,000
Tywin 30,000
Robb 20,000
Greyjoy 10,000
Stannis 2,000
Just under 35,000 men in two hosts of 20,000 and 15,000 for Tywin and Jaime respectively.
Chella daughter of Cheyk of the Black Ears had gone ahead to scout, and it was she who brought back word of the army at the crossroads. "By their fires I call them twenty thousand strong," she said. "Their banners are red, with a golden lion."
A Game of Thrones, Tyrion VII
"Twelve thousand foot, scattered around the castle in three separate camps, with the rivers between," her uncle said, with the craggy smile she remembered so well. "There is no other way to besiege Riverrun, yet still, that will be their undoing. Two or three thousand horse."
A Game of Thrones, Catelyn X
Tyrion also commanded an army of the Mountain clans of anywhere up to 3,000 men as the clans could have just wanted more stuff than they needed.
"First, though, I have some promises of my own to keep," he said as he sliced off a wedge. "I shall require three thousand helms and as many hauberks, plus swords, pikes, steel spearheads, maces, battle-axes, gauntlets, gorgets, greaves, breastplates, wagons to carry all this—"
A Game of Thrones, Tyrion VII
Robb's host consisted of 18,000 men.
Robb took it hard. "Mother, what are we going to do? I brought this whole army together, eighteen thousand men, but I don't … I'm not certain …" He looked to her, his eyes shining, the proud young lord melted away in an instant, and quick as that he was a child again, a fifteen-year-old boy looking to his mother for answers.
A Game of Thrones, Catelyn VIII
Catelyn then brings him an extra 1500 men from White Harbour so he has around 20,000 men.
Ser Wylis and his brother Ser Wendel followed, leading their levies, near fifteen hundred men: some twenty-odd knights and as many squires, two hundred mounted lances, swordsmen, and freeriders, and the rest foot, armed with spears, pikes and tridents.
A Game of Thrones, Catelyn VIII
Although not a total number of the Tully forces, as the Blackfish could have had more men, Edmure can muster 11,000 men.
"When all my strength is marshaled, I should have eight thousand foot and three thousand horse," Edmure said.
A Clash of Kings, Catelyn V
The Frey's mustered a host of 4,000 men and sent some with Robb but I can't find a number on how many that was or even if it was a different set of troops to the 4,000.
Lord Tywin's host was still many days to the south … but Walder Frey, Lord of the Crossing, had assembled a force of near four thousand men at his castles on the Green Fork.
A Game of Thrones, Catelyn IX
Renly has the biggest host of 80,000 men in his main army with another 10,000 at Highgarden. He also has some other unknown force at Storm's End.
"I'm told your son crossed the Neck with twenty thousand swords at his back," Renly went on. "Now that the lords of the Trident are with him, perhaps he commands forty thousand."
No, she thought, not near so many, we have lost men in battle, and others to the harvest.
"I have twice that number here," Renly said, "and this is only part of my strength. Mace Tyrell remains at Highgarden with another ten thousand, I have a strong garrison holding Storm's End, and soon enough the Dornishmen will join me with all their power. And never forget my brother Stannis, who holds Dragonstone and commands the lords of the narrow sea."
A Clash of Kings, Catelyn II
Stannis appears to only have 5,000 men when he get's to King's Landing and a similar number is said when he meets Renly too.
Lord Stannis himself was still on the march, but his vanguard had appeared two nights ago during the black of the moon. King's Landing had woken to the sight of their tents and banners. They were five thousand, Sansa had heard, near as many as all the gold cloaks in the city.
A Clash of Kings, Sansa IV
