Catelyn Stark successfully holding off an assassin that is attempting to kill her recently crippled son that is lying in a coma, with her even stopping a Valyrian Steel dagger with her bare hand.
Nymeria saving Arya by attacking Joffrey, and Arya taking Joffrey's sword and throwing it in the river.
When the Hound stops Loras Tyrell from being killed by Gregor Clegane. The Mountain, Westeros's One-Man Army is almost definitely the strongest man on the planet, stronger than even Hotah, Victarion, Andrik, Robert, Goghor, and Hodor, among others. Despite this, the Hound hops out of the stands and stops him. This is the only time one ever sees a warrior that is not a Fragile Speedster directly go head-to-head with Gregor and not lose awfully. After killing Mycah, this is the point when readers truly begin to sympathise with Sandor and the backstory he had.
It is even implied that Sandor could have won that fight.
Tyrion arguably becoming a Magnificent Bastard in his own right: He manages to escape certain execution by demanding a trial by combat and turns Bronn, a dangerous and highly skilled mercenary, to his cause. And when Lysa Arryn makes him go down a mountain pass inhabited by Proud Warrior Race Guys who have been the scourge of the Vale of Arryn for centuries, he manages to convince them to let him safely go through the pass and serve him as bodyguards and enforcers. And he actually upholds the promises he made to them instead of saying "Suckers!" once he's safely in his own army.
It gets better. The Promise he made was to ARM the Mountain Clans with steel armor and swords who then go back and use them to raid the Vale of Arryn. So he gets through the pass, gets body guards and enforcers, and his payment gets revenge on the woman who imprisoned him, all at the same time!
Unfortunately the clansmen use their new steel weapons not to attack Arryn forces but to raid & pillage hapless peasant villages, many of which are not even in the Vale but rather in the Riverland fringes. So in the end the smallfolk end up paying for Tyrion's scheme.
When the mountain clans get the drop on Tyrion and Bronn, they're outnumbered a dozen to two. Shagga tells his men to kill Bronn and bring Tyrion. Bronn's response of to draw his blade and ask who wants to die first.
A great one for Littlefinger is when he betrays Eddard Stark, saying "I did warn you not to trust me, you know."
Adds another layer of awesome when you look back at Cat's character and relationship with Littlefinger before her husband's death and realize that he would've had a chance at getting back with her if not for a Spanner in the Works by the way of Joffrey (Eddard was supposed to be sent to the wall, which involves giving up his wife.)
When foreign weapon-master Syrio Forel is confronted by five Lannister fully armoured men-at-arms and one of the knights of the Kingsguard, while he himself is armed with a wooden practice sword. The quote above was swiftly followed by the death of the men-at-arms. He only lost the fight because the knight had no gaps in his armor which Forel could use to kill him.
Never trust that a character is truly dead unless it is witnessed and confirmed by another POV character.
And even then...
While his morality is deplorable, one has to respect Gregor Clegane's might. He, and a dozen other knights, charges headlong towards an entire formation of Karstark spearmen. Despite almost all of the other knights being driven off or killed, Clegane powers straight through the spears and crash directly into the Karstark heavy infantry, probably killing four or five at least. Then, he rises, completely unscathed, and then begins to wield his BFS with a single hand, smashing every enemy in the vicinity into oblivion with contemptuous ease. Seconds later, the Mountain Clans pile in. Were it not for Clegane's sheer power, the mounted Clansmen might have been driven off by the spearmen, and the entire left flank might indeed have been driven off, as Tywin had originally planned.
Robb's continuing victories over the Lannisters, culminating in the climactic "King in the North!" moment at the end of the book.
Everything Eddard Stark did in a single book. His first action is to behead a deserter himself, proving that hands-on justice is the best kind. He has the honor to accept his bastard child Jon Snow, and his What the Hell King speech to King Robert when he orders that Dany and her brother killed to protect the Seven Kingdoms is a bastion of morality. And then he voluntarily gives up what could be considered the strongest political position in the entire world just to prove that he wouldn't go along with it.
With a little thinking it gets even better. He has virtually no experience with the Game of Thrones and yet he hurls himself in with no apologies whatsoever and is making headway to fix the kingdom. His actions motivate Cersei, Varys, and Baelish to accelerate their plans because they are afraid of him as Varys's discussion with Illyrio proves. In the end it takes a combination of Littlefinger betraying him, being high on milk of the poppy, wounded by Jaime Lannister, Robert dying, and (admittedly not too brightly) telling his intentions to Cersei. This is the kind of luck that could kill Xanatos himself and it took all that to bring him down. Not bad for the second son from a relatively isolated province.
Anytime that Dany humiliates Viserys, first by shoving him away and forcing him to walk behind the Dothraki khalasar for an entire day, then hitting him with a gold-plated belt. Considering that when we first see her she's merely a scared thirteen-year-old girl, this is some major character development.
Pretty much everything we see of Dany after her wedding sees her grow increasingly strong. The book ends with her hatching three dragon eggs on a funeral pyre, and succeeding, finishing by walking into the flames and carrying the dragons out again, almost entirely unscathed. And then she gets Jhogo, Aggo, and Rakharo to become her bloodriders, despite the Dothraki never allowing a woman to do this before. She came a long way.
Jorah defending Dany from Drogo's bloodrider. Epicness ensues.
Jorah: Horselord! Try me!
Jaime gets one off screen at Whispering Woods. His army is being tactically outmanoeuvred and overpowered by Robb Stark's ambush and he knows it. His response, the only thing that might still turn the tide of battle- he leads a charge at Stark himself hoping to kill him, cutting through dozens of men and would have succeeded and turned a resounding defeat into a victory with his personal prowess alone if he hadn't gotten his sword stuck in the corpse of one of Robb's bodyguards.
Jon showing off that he's more than just a good fighter by giving a speech to Maester Aemon to convince him to take on Sam as his assistant so as to spare him from Alliser Thorne's potentially lethal Training from Hell. Most of all this line, which shows a better understanding of the value of non-fighters than most of Westeros's Proud Warrior Race Guy culture:
“You can't hammer tin into iron, no matter how hard you beat it, but that doesn't mean it's useless.”