The climax of "Animal House", when the dragons all shield Hiccup, the other riders, Stoick and Gobber from the storm, and the animals slowly join them.
A minor one, but Mulch wheeling Bucket into the fortress via wheelbarrow and lamenting that Bucket is in too much pain to enjoy it as usual.
In the beginning of the episode, there's a moment when Astrid and Hiccup are competing in snow-racing where Hiccup smiles at Astrid when she's not looking. The look on his face is just adorable.
"I was thinking, all I needed was to get to Toothless. And together, we could make things right."
When Hiccup is kidnapped in "Alvin and the Outcasts", Stoick drops everything and goes to help him. After seeing what their relationship was like in the movie, witnessing Stoick as a Grade A Papa Wolf is very sweet.
Also Ruffnut and Tuffnut asking Stoick if they can personally beat Alvin black and blue for taking Hiccup. While the offer is declined, it was sweet of them. Especially since violence almost seems to be how they show affection.
Hiccup reveals himself to Alvin when he threatens Astrid.
The fact that Bucket went back to get a stuffed lamb for a little girl who was crying without it. Mulch quotes it best:
Mulch: Oh Bucket, your bucket is hard but your heart is soft.
Next episode, Gobber gets Stoick to agree to try Dragon Riding by pointing out it would help protect people from Alvin. Who wants to bet some of Stoick's instant agreement was more of the above Papa Wolf?
The second Stoick realizes the Thunderdrum is acting the way it has is to protect an injured friend, he instantly lets go of all animosity towards it and sends Hiccup and Toothless off for help while he waits alone to try and get along with "his" dragon.
It may seem a bit weird at first to watch Stoick help a dragon protect his mate so fiercely… until you remember Stoick is a widower. This means he wouldn't wish anyone, not even a dragon, to lose a loved one like he did. In other terms, he befriended Thornado because he identified himself to him, and this is Heartwarming In Hindsight.
Stoick's reveal that even if it doesn't seem like it, he has learned to listen to his son about dragons.
At the end of the same episode, it was just warming to my chest to see both Stoick and Hiccup riding together on their dragons.
A more subtle one from the same episode. When Hiccup protests that Toothless is his dragon, Stoick responds, "You picked a good one." Think about it. Stoick is acknowledging that Hiccup is capable of making good choices.
When Stoick was ready to quit learning to ride a dragon, Hiccup took him on a ride on Toothless, much like he did with Astrid in the movie. Hiccup mentions the beauty of the scenery, but Stoick instead talks about how good he feels seeing that the village and its people are safe.
At this point, all of episode 8, especially Stoick giving Hiccup a big hug near the end.
From the beginning, we have Stoick posing with Hiccup for the portrait, talking about how posing for the portrait with his own father had been a good day, and that this was as well. Sure, the portrait wasn't accurate, but one could argue it's how Stoick wanted Hiccup to be remembered. He didn't intend it as a slight. And he realized he'd messed up when Gobber pointed out possible reasons why Hiccup was engaged in such a dangerous treasure hunt.
Just a little moment during the posing. When Hiccup comments his chest really can't go further out than it is, Stoick simply says "Ah. Very well then." and claps him on the shoulder. Pre-movie, he'd have just told him to keep trying.
You could say "Portrait of Hiccup as a Buff Young Man" is an episode of a son trying to make his father proud of him. Sure, the movie strengthened the bond between father and son, but it's as though the show is digging deeper into their relationship. At the end of the episode, Stoick is crushed at the thought his son may have died, just like he was in the movie.
On the beach, Stoick openly, and with a tinge of pride, acknowledges that in one day Hiccup had made more progress than he and Gobber had in one month.
The Dragons all coming to the aid of their owners against the horde of fire-mouse dragons, without hesitation. Hookfang even goes over his shot limit in trying to protect Snotlout, and had to be helped by Meatlug.
When the new portrait is being put up, Hiccup takes a look at his father's hand on his shoulder and gives the smallest, but happiest smile.
Also, look at Stoick's expression on the two paintings: he's scowling and looking at buff!Hiccup with a rather worried expression on the first painting, but he gives him a big, happy smile on the second one. This little moment is probably courtesy of Bucket's subconscious.
Hiccup's closing narration.
Hiccup: I'd spent years trying to prove to my Dad that I was his kind of Viking. Turns out, I already was..
Stoick cuddling up to Thornado, and Hiccup doing the same with Toothless in "Dragon Flower".
Stoick: I spent my whole life trying to kill them...now look at me.
Also how he tenderly greets the sick Thornado: "How's my dragon warrior?" Just the tone of that line is heart-melting.
The entire episode, once again. Hiccup's determination to save the dragons and his promise to Toothless that everything would be okay is just the perfect display of the bond the two share. We've seen Toothless risk his life to save Hiccup, and now Hiccup gets to return the favor.
It's brief but, watching Toothless defending a wild Terror from Trader Johann was kinda cute.
Heather and her parents parting on good terms with Berk was a touching moment.
Also, after Astrid was the only one suspicious of Heather for the entire two-parter, she doesn't hesitate to save Heather's parents from Alvin. Then:
Astrid: I'm sorry I didn't believe you.
Heather: It's okay. I wouldn't have believed me either.
Hiccup throwing the Thaw Games so Snotlout wouldn't disappoint his father.
When Stoick announces the winner of the Thaw Games, he gives Hiccup a proud smile, showing that even though he didn't win, he's proud of him for making it this far.
The brief moment in Thaw Games when the twins realize they're each not on their usual Zipplback head, and help each other switch without complaint or fighting.
Doubling as a Call Back to the movie, Hiccup almost gets himself killed for Toothless again. He was willing to take a direct hit of electricity, knowing it could kill him, if it would save his dragon. It plays out like the movie with him drowning, but Toothless return the favor by breaking free of the same type of hold he was in the movie and swims down to get him.
Just before Hiccup and Toothless leave, Gobber addresses the dragon as "old friend."
Stoick running up the stairs once again and giving Hiccup a hug by lifting him off the ground.
Stoick and Gobber physically blocked the angry mob from a chained Toothless. They've come a long way. And when the mob advances, Mulch and Bucket stand with their chief.
"What Flies Beneath" is borderline Tear Jerker, with Toothless refusing to let Hiccup help him against the Whispering Death even though he can't fly without him. He continually prevents Hiccup from riding him, even shooting a plasma blast at him to keep him away (intentionally missing, but still), until his fight with the Whispering Death takes him to the edge of a cliff. Finally, Hiccup jumps off the cliff, and Toothless immediately abandons the fight to catch him. No matter how strained their friendship got, or how caught up Toothless was in his grudge, the moment Hiccup needed him, he was there. And Hiccup trusted him to be.
Toothless's behavior in the episode takes on a heartwarming tone if you take into account the events of the previous episode. Hiccup almost died for him, again; if the two episodes happened close together, Toothless was just trying to keep Hiccup from being in danger on his account again.
"Twinsanity" goes out of it's way to prove without a shadow of a doubt, Ruff and Tuff not only think alike (when they actually do think), they really do care about each other and their dragon.
A small example that reappropriates a Running Gag: Ruff and Tuff are often seen randomly headbutting each other - usually with one of them getting knocked over or briefly hurt. This episode shows that it's their own version of a personal handshake, and at the very end of the episode they do a small, non-violent one that's about as close to a hug as the two would ever get.
It's a smaller one, but Stoick was fully prepared to risk war with Dagur and the Berserkers just to defend Barf and Belch.
Not only that, but the moment Hiccup initiates his plan to trick the Berserkers, Stoick instantly goes along with it, despite having no knowledge of it beforehand. It shows a huge development in how at first in the movies and early of the series, he was skeptical of his son, but now has enough faith in Hiccup to execute his idea on a spur of the moment.
"Defiant One". Despite his method of greeting Snotlout when they are reunited, there's something heartwarming about seeing Hookfang eager to retrieve his regular rider.
After Hiccup and Snotlout escape from Outcast Island, Snotlout's suggestion that he and Hiccup should get some food is oddly touching. It's like Snotlout's way of acknowledging that he's accepted Hiccup at last is to act like they weren't fighting in the first place.
After working together with Toothless to get something Hiccup needs from a forge but before rescuing him, Snotlout jokes to Toothless that he might not be able to give him back to Hiccup since they worked so well together. Toothless quickly goes into angry-mode until Snotlout explains he was joking. That dragon loves his rider.
"Breakneck Bog" has Hiccup recovering the gift his mother made him.
While everyone else wants to run away, Astrid is the only one to never consider leaving Hiccup to find it alone. She even gets the others to stay with an Armor-Piercing Question.
Astrid: What if it was your mother?
The scene in the end is a culmination of an episode's worth of heartwarming. We find out what this gift is and what it means to Hiccup. In the show, it's a piece of his mother that he will cherish forever. With some Fridge Brilliance it is a symbolic representation of Hiccup's mother accepting his decision on living peacefully with dragons. The movie makes it plain as day that Hiccup has turned his back on the heritage that was expected of him. Recall that his mother's helmet was amongst the items that represented that life that Hiccup tossed away* This troper is aware that the same helmet becomes the plot trinket in Gift of the Night Fury that Toothless goes out of his way to get back when it gets lost. Nonetheless.... With the return of the gift, it acts as a way of Hiccup receiving approval from her, especially when it's revealed to be a stuffed toy dragon that Hiccup initially rejected.
You gotta admit Snotlout treated Gustav better than his mother (Granted he stole the eggs but Gustav's mother traded him for a supposed magical stone).
Hiccup really, really, really wants to find other Night Furies for Toothless to hang out with. Too bad they weren't where he thought they were...
Hookfang once again proves that, yes he cares for his rider just as much as any of the other dragons when Snotlout calls for his help. Hookfang spits flames at the Changwing holding his rider hostage and then he backs off the moment Snotlout asks him to do so.
The reunion scene between Hiccup and Toothless. The sheer happiness those two emit when they meet up again is enough to tug on the heartstrings.
Without any commands, the kid's dragons help Hiccup and Toothless without skipping a beat. It cements how much Hiccup means to them.
Yes, despite what it means (not to mention the evil laughter bit), you've got to admit Alvin bonding with the Whispering Death is was a surprisingly tender moment, seeing such a feared beast accept something it once considered prey to be an ally.
Pretty much the entire plot of "Flight Club" happened because Stoick was being an overprotective dad.
Hiccup and Astrid concern about Fishlegs in "The Iron Gronckle".
Gobber has a moment with Fishlegs as well. Specifically giving him the last Gronckle iron sword (The one he made for himself.) saying that anyone who takes down a outcast ship deserves one.
"Race to Fireworm Island". Proving that Snotlout has a heart, with how concerned he is for a sick Hookfang. No matter how much he denies it.
Heck Hookfang willingly giving up the one thing that could save his own life to try and protect his rider counts.
At the end of the episode we get a better understanding about why Hookfang would always be so rough with his rider, it's just tough love Monstrous Knightmare style.
In "Fright of Passage", the first thing Hiccup does after they've gotten rid of the Flightmare is to clear the good name of Astrid's family.
In "Zippleback Down", Tuffnut's genuinely affectionate bond with Torch, and the ensuing goodbye.
Tuffnut: I'm gonna miss you, Torch. You were the only one who ever listened to me.
Also a small one where he genuinely tries to have a conversation with Barf since he normally rides Belch and believes they haven't spent enough time together, once again showing that he does treat each head as a separate dragon.
The opening of the second part of "A View to a Skrill" where Hiccup refuses to give up the search for Ruffnut and Tuffnut.
In "Free Scauldy", Ruffnut bonds with a beached scauldron and names him Scauldy. When they run out of rope to for Scauldy's wing splint, she cuts off her braids to use as rope. As he swims back into the sea, she gives him a heartfelt goodbye.
Before that, Hiccup sadly decides that they'll have to leave the scauldron to his fate since he's too belligerent to be helped. The dragons won't accept this, though, and refuse to leave.
Stoick goodbye to Thornado is this and tearjerking.
From the season 2 finale we have the resolution of the Screaming Death dilemma, which involves: reuniting it with its mother, the Whispering Death held captive on Outcast Island. Both mother and child thank Hiccup before departing, screaming thank you to his face before flying off into the horizon!
Also from the season 2 finale; Stoick and Alvin reconciling after years of being enemies.