The venerable Lord Commander of the Kingsguard, Ser Barristan Selmy makes my list as the #4 Greatest Warrior of the Westeros. Advanced in age for a warrior, but showing no signs of slowing down Ser Barristan certainly lives up to his moniker of "The Bold".
#4-Ser Barristan Selmy
Ser Barristan is revered, nay beloved by the highborn and smallfolk of the Seven kingdoms alike. He is the type of knight that fits the rommance, the ones that Sansa dreams about. At the time of the War of the Five Kings he is the Lord Commander for King Robert Baratheon and had served under the Mad King Aerys, presumably as a knight rather then Lord Commander. I say this because at the time of the Tower of Joy, the Lord Commander was Gerold Hightower. Gerold was actually at the Tower and was slain so it's unclear when Barristan became Lord Commander. He was pardoned by Robert after the Trident, so it's possible that there was a gap between Gerold and Barristan.
After the pardon he serves Robert as Lord Commander until dismissed by Cersei after Robert's death. This has a profound effect of him, denouncing the Baratheon heir (actually Lannister heir when you look at it) and setting out on the road of seeking Daenerys. The best part of his dismissal is his frank appraisal of Joffery and the fact that he takes crap from no one over it. When the pathetic Gold Cloaks of the City Watch of King's Landing (aka "Red Shirts") arrive to arrest him, he dispatches them and disappears until turning up in A Feast for Crows.
Ser Barristan has been a member of the Kingsguard for ages it seems as he joined when he was 23 He earned his nickname by taking part in a joust at the age of 10 when he was still a squire after acruring some armor.
He defeated Prince Rhaegar at the Tourney at Strom's End and even The Hound in another joust so his skill is not to be doubted. And on top of all of this he was knighted at 16. He is most likely a prodigy as a knight by any sense of the definition.
Much like some of the other characters in the book we get a sense of his prowess only through the past. But like other mighty warriors he is seen as outstanding example of knighthood and a great warrior. Slaying Maelys the Monstrous probably doesnt hurt your knight cred either. Barristan is not one of those "deep history" characters but from a generation prior, a generation prior to Robert/Ned's generation. But it's important to note that everyone who talks about his prowess is united in their praise.
The interesting part is that he is not caught in the "crossfire" of having served The Mad King, which was responsible for Robert's Rebellion through his actions. Presumably the Kingsguard do just that: guard the king, not judge him. This is alluded to by Jaime when he talks about slaying Aerys. Perhaps Ser Barristan's fame is beyond reproach.
We do not however get a sense as to what kind of leader of men he is. Being a member of the Kingsguard presumably precludes a lot of this as his primary role is the protection of the king. The fact however that he survived the Trident when many didn't is important to note.
As an aside one gets the sense that Barristan is set in the mold of William Marshal. He is a renowned tourney fighter like Marshal and a warrior par excellence. Given Martin's perchance for "borrowing/being inspired by" history I think this is quite the case. Ser Barristan is a noted jouster and successful having fought in the War of the Ninepenny Kings. Again echoes to William Marshal: successful in war and tourney. Having fought in the Ninepenny War one wonders how familiar he is with Brynden Tully (at #10 on this countdown).
I feel comfortable with where Ser Barristan is here: beloved by the high and low in the Seven Kingdoms and with the prowess to back it up, even at the age of 57. He is one of the finest blades of the realm and fitting that he appears at #4.