Blink and you'll miss it, but Galahad was going to sacrifice himself to save the team. Eggsy's father pushed him away and did the Heroic Sacrifice himself.
Galahad informing little Eggsy and his mother about the death of the former's father and the latter's husband. He even gives them a Kingsman pendant that will grant them one request.
The growing smile on Eggsy's face when Galahad talks to him about his father.
Galahad bringing Eggsy to the Kingsman, and telling him why he chose him:
"What do you see?... I see a young man with potential, a young man who is loyal, who can do as he's asked, and who wants to do something good with his life."
In a very strange way, the relationship between Valentine and Gazelle. The former is respectful and can depend on her; the latter is loyal and, in her own way, sweet to him.
They even share a hug after having dinner with Galahad.
And Valentine gives her butt a lil' pat as she's heading up the stairs.
After Valentine shoots Harry in the head, Gazelle quickly comforts him. Albeit, she does try to convince him that killing was great, it's rather sweet nonetheless.
Gazelle is also the only person in Valentine's fold who he didn't plant a chip in.
Before going of for her climactic fight with Eggsy, she cradles Valentine's face in her hands for a brief second.
Valentine's genuine displeasure in killing Harry. Oddly enough, he's content with unleashing mass genocide, but directly taking a life proves to be too much for him. He even stated that it felt terrible, and asked if Harry was actually dead.
Harry taking Eggsy to the Kingsman Tailor shop, showing him various cool gadgets and getting him fitted for a suit is reminiscent of father-son bonding.
Eggsy intentionally hitting another car in order to avoid hitting a fox, then allowing his friends to escape and refusing to give up their names under threat of jail time foreshadowing his loyalty to those who are good to him.
Although their interactions are short, Eggsy is shown to be a caring, Cool Big Bro to his younger sister.
To make it even better, considering that Eggsy was still an only child when his father died 17 years ago, that means his sister is actually Dean's kid. Eggsy loves and cares for the daughter of a man he hates, and harbours no ill feelings toward her at all—even as her own father ignores her and makes Eggsy's everyday life a living hell.
Harry stuffing his dog, Mr. Pickles. Somewhat morbid, but still quite thoughtful. As are the circumstances.
Harry: No, I shot my dog, and then I brought him home and continued to care for him for the next eleven years until he died of pancreatitis! It was a blank, Eggsy!
Roxy protecting Eggsy from the bullying of the other Kingsman candidates.
In reciprocation, Eggsy encouraging and supporting Roxy during the skydiving test, and eventually when she has to go to the edge of the atmosphere to destroy Valentine's satellite.
Eggsy's inability to shoot his own dog, and later, his refusal to believe that he was weak for it.
Eggsy and J.B.'s relationship is utterly heartwarming and funny. At first he gets J.B. thinking he's a bulldog when he's actually a pug, meaning J.B. won't grow any bigger or threatening. While training they bond; Eggsy while running with J.B. yells at him to move, saying that he can't carry the pug; he then tucks J.B. into his vest and keeps going. J.B. sits smugly as Eggsy does so.
When Arthur offers Eggsy a place in Valentine's new world, he thinks it over and defiantly says "I'd rather be with Harry. Thanks."
The fact that it's very clear that Eggsy loves his mother and is trying to protect her from her abusive husband. When he tries to fight him at the pub, it's very clear that he wants to fight him, even in spite of the taxi being driven by the tablet. At the very end, he invites her to live with him in his house and even gets into a Galahad-style bar fight to protect her.
Beforehand, Eggsy's mother comforting her daughter after being released from the Hate Plague which brainwashed her into nearly killing Daisy, which sets the tone in stone that despite her flaws she loves her children. Much earlier, there's also her trying to protect Eggsy from the wrath of her new husband, making it evident that her children will always come first.
The text after the final scene shows that Matthew Vaughn dedicated the film to his mother, Kathy.
The reveal that, in the end, the Kingsman candidates were never in any true danger at any point during their training. Merlin might be a Sink or Swim Mentor, but it's clear he really loves his students and is willing to die for them.
After the skydiving test, Eggsy angrily confronts Merlin about him being the "gimp". Instead of scolding him for being rude, Merlin simply tells him to step closer and says, in his own way, that Eggsy is just as valuable as everyone else. The little smile on Eggsy's face when he realizes he had a parachute all along—and that at least one person doesn't see him as an expendable candidate—just seals the deal.
Merlin: You need to take that chip off your shoulder.
When Eggsy successfully saves the day along with Roxy and Merlin, what does Merlin tell him? "Harry would be proud of you. He was right."
The origin story of the Kingsman, incredibly rich men having brought their wealth and resources together to protect peace and preserve life for the greater good after losing their heirs in World War I. The Kingsman may have been started out of self-interest, but clearly the initiative works for the good of all.
