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.
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.
Thor getting Jane's notebook back from SHIELD, then the scene where he teaches her about The World Tree and the nine realms.
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.
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."
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.
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!"
Big. Damn. Kiss.
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.
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!"
The ending, which has Thor walking up to Heimdall at the destroyed Bifröst, and asking about Jane. "She seeks you." (Sniff.)
Even after all Loki has done, Thor and Odin are still devastated when they think he is dead.
A Deleted Scene where Thor and Loki talk right before Thor's coronation.
Loki: I've waited for this day as long as you have. You are my brother and my friend. I may sometimes be envious of you, but never doubt that I love you.
Of course, knowing what comes afterward and that Loki purposefully ruined Thor's coronation does make this scene a bit of Tear Jerker.
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: One day, I shall make you proud. Odin: You've already made me proud.
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.
"Guards! Someone! HELP!" Loki goes from yelling at Odin to panicked calling for help as soon as his father falls unconscious.
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.
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.