The Minor Kidroduction with Odin, Thor and Loki at the beginning. The both of them are listening enthusiastically to their father's story and are so excited when he tells them that they both were born to be King.
A Deleted Scene where Thor and Loki talk right before Thor's coronation.
Loki: I've looked forward to this day as long as you have. You are my brother and my friend. Sometimes I'm envious, but never doubt that I love you. Thor:[claps Loki on the shoulder] Thank you.
Loki is sensing how nervous Thor is and lights up the mood by jokingly mocking his helmet. The moment where Loki is trolling the servant by scaring him with illusions of snakes becomes especially heartwarming in hindsight when we find out in Ragnarok that Thor loves snakes.
And this exchange:
Thor: Seriously, how do I look? Loki: ...Like a king.
Of course, the whole scene takes a darker tone when we find out later that Loki had already given the Frost Giants the information they needed to get into the weapons vault and "ruin Thor's big day."
In the extended version of the scene where Thor declares that they are going to Jotunheim, Thor tries to persuade Sif and the Warriors Three to join him by asking if they're going to let him and Loki take all the glory. Heartwarming for several reasons: Thor, the arrogant warrior prince, not only automatically expects Loki to share the credit of a victory, but also assumes that Loki would come- whereas he laughed off the others' objections, Thor looks almost vulnerable at the idea of going without his little brother. Then there's Loki's response: a surprised, almost gratified smile. You really get the feeling that they do care about each other, and that Loki never really wanted the throne for himself — he just didn't want Asgard to have a reckless king, which Thor admittedly would have been, if not for his experiences on Earth.
Thor: My friends, trust me now- we must do this! You're not going to let me and my brother take all the glory, are you? Loki: What...? Thor:[face falls] What, you are coming with me... aren't you? Loki:[smiling] ... Yes, of course. [stands] I won't let my brother march in Jotunheim alone!
There is something heartwarming about Thor supporting Sif in becoming a warrior despite being a woman, especially since he started off as an arrogant prince and this event happened before the movie.
All the moments displaying Thor and Sif's bond in a more subtle way were rather well done in this aspect. Him supporting her desire to become a warrior, their individual reactions to the other getting killed/about to get killed by the Destroyer, her happiness about being reunited with him or seeing him be revived, him trying to convince her to retreat since he knows she'll sacrifice herself and die if he doesn't, her troubled expression as she is one of the few people who notices and recognizes that Thor is grieving at the end of the movie, etc. The fact that the writers intentionally used those scenes to hint that there might be more to Thor and Sif then just friendship is simply icing on the "aww, look, they do care" cake.
Jaimie Alexander:[regarding the possibility of romance] But there is a reason that we sort of subtly hinted to it in the first film. Just so that there is a door. If we want to go through that door we can. They like to cover all their bases over at Marvel.
Loki, during Odin's rant at Thor, notably tries speaking up for Thor. Sure, Odin's growl-roar-thing at Loki is funny, but it is still heartwarming to see Loki try to stand up for his brother.
Especially the utter ease with which Loki tries to interpose himself, once you think about it... Loki's gotten used to playing peacemaker between his brother and his father.
When Odin tells Loki about his real parentage, we see a short flashback of Odin finding Loki in Jötunheim. The scene is an example of superb editing, because as soon as baby Loki is changed from his Jötun form to his Aesir form, he stops crying and even starts to smile at Odin. Doubles as tear-jerker, in contrast to the scene that initiates the collapse of their relationship.
It gets even more heartwarming: Odin is gently caressing him to make him stop crying, and smiling down at him with genuine affection. This shot alone contradicts Loki's conviction that Odin only saw him as a war relic from the beginning.
"Guards! Guards, please, HELP!" Loki goes from yelling at Odin to panicked calling for help as soon as his father falls unconscious.
The extended version of the scene with Loki and Frigga at Odin's bedside has Frigga telling Loki "You're a good son." In this same extended scene, Loki is, to his utter surprise, given Gungnir and declared king. The heartwarmer there is two-fold: one, Loki really wasn't doing all this to get the throne — becoming king wasn't even something he'd considered and two, Frigga then tells him "Make your father proud." Though considering what he hopes will make his father proud...
The theatrical version of this scene is still quite heartwarming.
Loki: So why did he lie? Frigga: He kept the truth from you so that you would never feel different. You are our son, Loki, and we your family.
Becomes Fridge Heartwarming in The Avengers: Loki's come to hate both Odin and Thor, but he doesn't include Frigga in his diatribe. Even Bad Men Love Their Mamas indeed.
Anytime Thor does the I Kiss Your Hand maneuver. It's just really, really charming.
Especially the first time. Thor has spent most of his time on Earth raging and cursing and doing nothing but causing Jane, Selvig, and Darcy trouble. But when Jane decides that she can't be involved anymore and tells him that she's sorry but she can't give him a lift to where he's going, he politely thanks her for all of the kindness she's shown him thus far and just kisses her hand. It's topped off by Jane's expression, like she can't believe someone would do something so gentleman-like for her.
Selvig and Thor sharing a drink together, with Selvig offering Thor some advice after Thor admits that he has no idea what to do now.
"We drank, we fought, he made his ancestors proud!"
Thor gives Jane her notebook that he took back from SHIELD. Then Thor tucks Jane into her cot as they both look up in the sky and Thor tells about Yggdrasil and the Nine Worlds to an enthralled Jane.
Thor getting the notebook is doubly sweet because he doesn't exactly know who Jane is or what her job is or why the government would take her stuff. All he knows is that the notebook and equipment mean a lot to her and her work and that it's his fault that she lost it.
In the extended version of that scene, he goes back to the diner where he smashed the coffee mug and offers the proprietor a replacement. Small and sweet. Also props to the proprietor who responds very positively to Thor's clearly sincere apology and as he takes his leave, remarks that "(Jane) could do worse (than him for a Love Interest)"
In the extended scene where Sif and the Warriors Three searches for Thor on Earth, Volstagg helps a little girl retrieve a baseball underneath a car. Instead of being scared of the Asgardian warrior like the adults were in town, the little girl shows gratitude by saying "Thank you" to Volstagg.
The Warriors Three, Sif, and Thor being reunited. They're all so happy to see each other again.
Repeated and amplified a short while later when Thor regains Mjölnir and his godly power. The shift from the utter anguish of having thought he was dead to the unbridled joy at seeing him restored really sells it.
Even though it's hopeless, Sif wants to continue fighting the Destroyer and die a warrior's death so that stories will be told later of that day. Thor says to her "Live, and tell them yourself."
Big. Damn. Kiss.
In a rather nice blink-and-you'll-miss-it moment: just after Thor gets his power back and he and the others get ready to go back to Asgard. Look closely and you'll see Fandral and Darcy holding hands and smiling at each other before he joins Thor and the others. You've got to admit despite his nature, it was a rather cute little moment.
In spite of Odin concealing his identity as a Frost Giant from him, when Loki kills his biological father, Laufey, he declares himself as the son of Odin.
When Thor decides to stop Loki's plot by destroying the Bifröst Bridge, he protests because Thor will be unable to reunite with Jane.Of course, he is a very manipulative liar, so he might have just been trying to stop him for his own reasons.
Manipulative liar or not, when people panic they usually end up saying the first thing that comes into their head. With that in mind, you have to admit it's slightly heartwarming that this was what Loki first thought of instead of, "I need that!"
Thor saving Jotunheim from destruction. After starting out with all that contempt and instilled hatred of the Frost Giants, after character development Thor would fight and risk never seeing Jane again to save the species.
Even after all Loki has done, Thor, Odin and Frigga are still devastated when they think he is dead. Even Sif sorrowfully expresses her condolences to Frigga.
Thor and Odin's reconciliation toward the end;
Odin: You'll be a wise king. Thor: There will never be a wiser king than you. Nor a better father.
Thor: Perhaps one day, I shall make you proud. Odin: You've already made me proud.
The ending, which has Thor walking up to Heimdall at the destroyed Bifröst, and asking about Jane. "She seeks you." (Sniff.)