Stannis declares that Theon is to be executed and a raven on a nearby table starts to freak out and scream Theon's name, despite most ravens not being smart enough to know words without being taught. The most likely conclusion is that Bran is warging in it and is upset by Theon's impending death.
There's a small moment where Theon remembers Jeyne's happiness at being rescued.
"You saved me," Jeyne had whispered, as he was carrying her through the snow. She was pale with pain, but she had brushed one hand across his cheek and smiled.
Stannis orders that, should he die before the war is over, his soldiers keep fighting and sit Shireen on the Iron Throne or die in the attempt.
Aeron Greyjoy's preview chapter is pretty horrifying from start to finish. But when Euron has his would-be salt wife, Falia Flowers tied to the prow of the Silence next to the Damphair, Aeron offers what little comfort he can. Made even more heartwarming when you remember earlier in the chapter, Falia had defied Euron and secretly brought Aeron some honeyed oatmeal to eat instead of the rotten meat Euron had been giving him. No doubt Aeron remembered that kindness.
Aeron: Falia Flowers, have courage, girl! All this will be over soon, and we will feast together in the Drowned God's watery halls.
This may also count as a moment of awesome, as despite all that Euron has done, Aeron still maintains his Faith in the Drowned God. Fucked up as that faith is, that takes determination.
In Sansa's preview chapter, Lothor Brune nicknames Alayne's new betrothed Harry the Heir "the Arse" after he's been rude to Alayne calling her a bastard in her face. And Sansa is so grateful for this comment, that she hugs him. This moment is so similar in tone & content to a caring uncle comforting a distressed niece.... a role that the Blackfish once played to Sansa's mother, aunt & uncle. And it fits with Ser Lothor being one of the few men in Littlefinger's service who is a genuinely well meaning man.
In Arianne's preview chapter she wishes she could reunite with her little brother Quentyn after she found out he never plotted to rob her of her birthright. Doubles as a Tear Jerker as she never will. He's already dead.
Also she makes clear to her bastard little cousin Elia that no matter if she's a bastard, the Prince her uncle would never turn his back on his brother's daughter. The Martells are not perfect but are a loving family anyway and while Doran is no saint, he's a far more decent man than the equally powerful Tywin Lannister.
Daemon Sand holds some grudges to Arianne and her father since he was denied her hand but you could tell his true feelings by the fact he's now Arianne's sworn shield and he's willing to go to a risky mission in her place.
Before she married Viserys I Targaryen and went full Lady Macbeth, Alicent Hightower was a simple maidservant for Viserys' grandfather, Jaehaerys I, being his primary caregiver during his last days. She comforted him, and he would compliment her, in the process mistaking her for Saera, his long-disowned daughter who went to Essos and never returned, even for her father's death. Years later, when Alicent started slipping into insanity during her imprisonment after the Dance of the Dragons, she would reminiscence about Jaehaerys' compliment.
I want to see my sons again, and Helaena, my sweet girl, oh ... and King Jaehaerys. I will read to him, as I did when I was little. He used to say I had a lovely voice.
Aegon III lived a pretty sad life, but the best thing that ever happened to him was getting his younger brother back. Everyone believed that Viserys II had perished in the Battle of the Gullet, and Aegon suffered from Survivor Guilt because he'd had a dragon to escape on but Viserys hadn't. Years later Viserys turned up alive in the Free Cities, having been taken hostage by merchant princes. Alyn Velaryon recovered him, brought him back to Westeros, and reunited the two brothers. It's said this was the only thing that ever brought Aegon true joy, and Viserys was the only person he trusted fully.
King Baelor walking through a pit of vipers to free his cousin, Aemon the Dragonknight, with full confidence that the Seven would protect them. He was wrong about the Seven protecting them, but it was still a valiant feat. And for that matter, his treatment of the Dornish. He released their hostages and walked thousands of miles to Sunspear from King's Landing barefoot in a show of humility. On the king's way back, the Prince of Dorne, fearing that Baelor's death would threaten the new peace, commanded his bannermen to be as accommodating as possible.
Baelor's kindness to the Dornish would be posthumously rewarded twenty years later when King Daeron II worked with his brother-in-law, Prince Maron Martell, to formally unite Dorne with the Seven Kingdoms, the capstone to which was to lay a golden wreath before Baelor's statue and declare:
"Baelor, your work is done."
Ser Duncan the Tall, a lowborn hedge knight is to stand trial by combat for having attacked a member of the Targaryen royal family in order to protect a lowborn puppeteer woman who was being assaulted by the aforementioned Royal Brat. A large crowd gathers to watch the trial and Duncan wonders about why so many people would like to see his death. Then the smallfolk start issuing words of support, cheering for him, some women kiss him to wish him luck and a septon even blesses his sword.. He is in disbelief. "They are for me? Why? What am I to them?" His companions reply, "A knight who remembered his vows."
Aegon the Unworthy once hosted a tourney and forbade Aemon the Dragonknight from entering because he wanted to name his mistress Queen of Love and Beauty. Knowing that Queen Naerys would be humiliated, Aemon entered the tourney anyway as a mystery knight known as the Knight of Tears, won, and crowned the queen instead. There's another layer of heartwarming to this. It's rumored that Aemon and Naerys were in love and would have rather married each other. If this is true, Aemon wasn't just looking out for his sister, he was defending the honor of the woman he loved.
During Aegon's Conquest, Queen Sharra Arryn returned to the Eyrie's throne room to find her young son Ronnel, the last king of the Vale, sitting on Queen Visenya Targaryen's lap, asking his mother if he could go for a ride with the lady and her dragon. Not very heartwarming in itself, considering the Adult Fear Sharra must have experienced, but the touching moment came after. Once the Vale surrendered to Aegon, Visenya actually did take Ronnel for that ride on her dragon, Vhagar. Three times. It earned him the nickname 'The King Who Flew'. It could be seen as a Pet the Dog moment for Visenya. Her reputation in Westeros is one of a somewhat stern Lady of War with a manipulative streak who possibly murdered her nephew/stepson Aenys I to put her son Maegor (AKA Maegor the Cruel) on the throne. Yet she had enough of a soft spot to take a little boy for a fun ride through the sky.
Egg sitting at Dunk's bedside after he gets knocked out by Ser Uthor in "The Mystery Knight", as well as his relief when he sees him again.
Egg: I knew no stupid snail could kill you, ser.
Prince Peremore Hightower was a Genius Cripple who had an insatiable curiosity for the world around him. He'd bring scholars, healers, priests, and wise men to Oldtower because he loved to listen to them argue over academic topics. After Peremore died, his older brother King Urrigon gave a tract of land to those scholars so they could continue their quest for knowledge, thus founding the Citadel. This all but outright states that Urrigon wasn't ashamed of his brother for being disabled or bookish like most people in Westeros would be, but that he instead supported Peremore's intellectual pursuits and wanted to honor him.
Sansa hearing that her brother Jon has been elected Lord Commander of the Night's Watch, and wistfully thinking how so sweet it would be to see him again. Prior to their family being separated, Sansa dreamt so much of being a princess betrothed to a prince at court and after all the hell she's been through since she's been separated from her family, it's both heartwarming and tearjerking whenever she fondly thinks of her siblings and of home.
A minor scene but once Bran mentions that the statues of the tombs in Winterfell are usually reserved only for the Stark kings and lords, it reminds us that Ned's deceased siblings, Brandon and Lyanna, have their own statues next to their father Rickard thanks to Ned insisting to have them carved. It really shows how much love Ned has for them as well as doubles as a Tear Jerker over the fact they have died rather young.
In a heartwarming-for-a-Lannister type way, Tyrion has clearly known about Cersei and Jaime's romantic relationship for quite some time, yet has never used the information against them. Contrast with the nanoseconds that it took both Lord Tywin and Cersei to use knowledge of Tyrion's personal life to try to manipulate him.
Any time the Stark children reminisce about each other and Winterfell. It shows just how close-knit this family was and the love they have for each other.
Arya: Suddenly Arya remembered the crypts at Winterfell. [...] When the spirit stepped out of the open tomb, pale white and moaning for blood, Sansa ran shrieking for the stairs, and Bran wrapped himself around Robb's leg, sobbing. Arya stood her ground and gave the spirit a punch. It was only Jon, covered with flour. "You stupid," she told him, "you scared the baby," but Jon and Robb just laughed and laughed, and pretty soon Bran and Arya were laughing too. The memory made Arya smile, and after that the darkness held no more terrors for her.
Bran: Back in Winterfell Sansa had told him that the demons of the dark couldnt touch him if he hid beneath his blanket.
Sansa: She remembered a summers snow in Winterfell when Arya and Bran had ambushed her as she had emerged from the keep one morning. Theyd each had a dozen snowballs to hand, and shed had none. Bran had been perched on the roof of the covered bridge, out of reach, but Sansa had chased Arya through the stables and around the kitchen until both of them were breathless. She might even have caught her, but shed slipped on some ice. Her sister came back to see if she was hurt. When she said she wasnt, Arya hit her in the face with another snowball, but Sansa grabbed her leg and pulled her down and was rubbing snow in her hair when Jory came along and pulled them apart, laughing.
Jon: He thought of Robb, with snowflakes melting in his hair. He thought of Bran, clambering up a tower wall, agile as a monkey. Of Rickons breathless laughter. Of Sansa, brushing out Ladys coat and singing to herself. He thought of Arya, her hair as tangled as a birds nest.
A meta example. A thirteen-year-old fan tried donating all his £153 savings in order to get a grisly death in the books. Martin was touched by the man's effort, and instead of granting him a grisly death (since all the spots had been filled by that point) he donated $10,000 in the boy's name to a wolf conservation scheme, wishing him luck in his future endeavours.
When Mad King Aerys demanded that Robert Baratheon and Ned Stark, the two young men who he helped raise, be brought to him and executed, Jon Arryn raised his banners and ignited the rebellion.
Another Robert's Rebellion example. The cassus belli is definitely kidnapping of Lyanna Stark. Stark (Ned, Brandon and Rickard) raise arms to rescue their sister/daughter, Robert Baratheon did the same to rescue his beloved and Jon Arryn to protect Robert and Ned. While many people lost their lives, The things I do for love indeed.
Results of Davos smuggled supplies to blockaded Storm's End at Robert's Rebellion.
First, Stannis cut three of his fingers and knighted him. Also making him his friend.
Definitely hungry Stannis lets the weak ones eat first and himself last. When Stannis says he does his duty, to the kingdom or to his men, he means it.
Ned Stark loved and raised his illegitimate son, Jon Snow, just like his trueborn children and brought him up alongside them, wherein Jon developed loving and close relationships with his father, half-siblings, uncle and many at Winterfell — while many other nobles would have their illegitimate child fostered elsewhere and financially support them from afar. At worst, some nobles neglected their illegitimate children rather then caring for them and refuse to acknowledge them until there is no other option (like Ramsay and Roose).