The greatest of all is situated in the backstory: fourteen-year-old Jon Snow finds himself stranded in Skyrim, barely able to speak the local dialect, his only possessions being his direwolf and the clothes on his back. He proceeds to claw his way to the top, becoming Grand Thane of Skyrim, helping the Empire to win the Civil War, slaying the World-Eater and kicking Miraak's ass to Oblivion. All hail the Last Dragonborn!
Enzo Vlast the Ebony Knight tried to go out gloriously by fighting Jon to death. The duel lasted half a day and left both opponents half dead. Enzo then decided he would serve Jon instead.
Catelyn — literally the last person you would expect helping Jon — outright tears into Ned for stubbornly wanting to pressure Jon into staying in Westeros, seeing right through his bullshitting justifications and shocking him into a Heel Realization.
Ser Barristan Selmy is actually hinted to have guessed the Family Relationship Switcheroo pulled by the Starks without any prompting — by mere virtue of being such an intimate friend to Rhaegar, he immediately recognizes Jon's Beautiful Singing Voice as the Silver Prince's.
Poor little Shireen is bullied and intimidated by the Queen, until Cersei throws a demeaning comment on Davos Seaworth. The girl immediately fires back that Davos is perfectly worthy of being her regent.
Sandor Clegane and Enzo briefly team up against the Mountain that Rides on the tourney.
Tywin Lannister verbally bitchslaps Cersei for being such an incompetent dumbass, while threatening to murder her Axe-Crazy eldest son if he doesn't shape up in six months.
Bran savagely demolishes his eldest sister and mother in quick succession — first telling Sansa that no, she's not entitled to Jon's affections then parrying Catelyn's argument regarding a bastard's untrustworthiness with historical precedents of loyal baseborn siblings and depraved trueborn kings. Both Sansa and Catelyn are left unable to defend themselves further.
Jon killing 10 people (two Kingsguards and eight Lannister guards) before the latter can attack him. And then killing Gregor Clegane.
Bitchslapping Sansa when he finds out that she told Cersei about the Starks leaving.
Serana crushing a soldier's head (and helmet) against the wall in one move, throwing another out of the window and crushing the throat of the last one. Then saving Sansa and later Myrcella from being captured.
Valerica dealing with the Lannister guards is such a Foregone Conclusion that the author doesn't even show it. But we do get to see her giving the a Grin of Audacity and telling them to Bring It. She is next seen splattered head to toe with blood and completely unharmed.
Sam tackles a guardian that was mishandling Shireen, showing great bravery and nerve in what is clearly a horrific situation. He may be considered a coward because he doesn't defend himself, but when someone else's life's in danger he'll jump in without hesitation.
Myrcella killing Joffrey in retaliation for Tommen's death.
Enzo single-handedly saving Dustun and Dalla from the Lannister thugs trying to kill them, first by destroying the first three and then sending a dozen more flying with a FUS RO DAH!
Syrio arrives later, killing one guard of a group that has cornered Arya and Gendry, and sets out to prove why he's the former First Sword of Braavos - this time using an actual sword.
One Lannister guard manages to grab Arya after stabbing her in the shoulder. Arya answers by blasting frost magic in his face.
When Arya falls to the Blackwater, an Argonian jumps right behind, kills the guard that tackled her in with nothing but his teeth, and puts a Water Breathing ring on her, saving her from drowning.
Jon gets Mhaegan and Barra to the docks, when three Lannister guards appear and attempt to kill them. Jon uses the Fire Shout on them.
One of the guards survives and attempts to kill Mhaegan - but before Jon can act, Ser Barristan Selmy appears and kills the guard.
When Cersei tries to kill Tyrion during her coup, he uses an oil lamp to set her on fire.
The ship taking everyone out of King's Landing finally departs, but the Royal Navy is sent after them. Jon has everyone but the sailors go below the deck and busts out the Storm Shout, sinking the royal ships before using the Clear Skies Shout to ensure their ship will get away.
Jon is limited to three Shouts at day, four if he pushes himself, yet he exceeded that in order to use the Clear Skies Shout. Sure, he starts coughing up blood and immediately blacks out afterwards, but it's nonetheless impressive.
After getting outed as a Targaryen, Jon gets attacked by a knight bent on extinguishing the Mad King's bloodline. The Dragonborn easily curb-stomps the man... then helps him to get back on his feet instead of slaying him, because he's far better than this.
The Northern banners meet to discuss their next course of action. Here Robb proves himself a born Lord, expertly navigating the many strong personalities of the gathered nobility. He easily settles an argument on who should build a fleet by logically delegating the task to those with the knowledge and ability to do so. While also satisfying his other vassals by having the Umbers provide lumber, thus a share of the prestige.
When Lord Chyttering tries to cast shadow on Ser Davos on account of his checkered past as a smuggler, Shireen puts him in place by pointing out that Ser Davos not only faithfully served her father and now her, but he was also by her side as they escaped King's Landing... which she cannot say for Lord Chyttering.
Alerie Tyrell faints in the middle of a tense confrontation with a group of Tarth men, and falls into the water. One of the latter jumps in to save her, still clad in heavy armor, and brings her back out with ease. This is, of course, Brienne of Tarth.
