Thor and Jane's reunion, after she stops slapping him.
Meta example: Natalie Portman wanted to return for this movie and signed on, but couldn't work on it at the time due to being on Maternity Leave. What did the production team do? Why, hold off on making the movie until she could participate, of course!
Frigga's relationship with Jane and protecting her from Malaketh to the point of sacrificing her own life. It's been established that Jane's relationship with Thor is futile due to her much shorter lifespan, but Thor's mother will defend her because she is the woman her son loves. Doubles as a Tear Jerker.
Sif and Volstagg being protective of Thor was just precious.
In the scene where Jane is being examined, Jane and Thor keep exchanging smiles.
More specifically, when Jane correctly guesses that the tech above her is a quantum generation field, Thor's proud that's-my-girlfriend smile is just adorable.
When Odin takes Thor and Jane into the library, explaining about the Dark Elves, Thor recalls the story in saying, "Yes, Mother used to tell us stories as children." Us, as in, he and Loki. It's small, but it shows that Thor hasn't forgotten his brother or the times they spent together.
The very fact that Loki still cares about Frigga, and was very willing to join Thor in avenging her.
Frigga and Loki's entire relationship - she begs Odin to spare him, and then visits him in his cell against her husband's wishes, bringing him books and trying to make him comfortable. She's the only one in the movie Loki seems to value and doesn't lash out against. It's also very telling that she's the one who taught him magic - young Loki must've felt very insecure under his father and brother's shadows, and Frigga gave him something that was his own.
When they're in the Dark Realm and Jane is still unconscious, Loki starts to question Thor on him choosing her; he says that she's like a moment in their long lives, and will be gone before Thor knows it. What makes this heartwarming is that Loki appears genuinely concerned about his brother, knowing that Jane will only cause him heartbreak.
In the same scene, after Thor and Loki have an argument about Frigga, this exchange happens which is both heartwarming and giggle-worthy:
Thor: No... [Mother] would not want us to fight. Loki: ...Well, she wouldn't exactly be shocked.
Right after that, Thor gives him a small fond smile. And if you look close enough, you would see Loki giving him an even smaller one.
And despite everything, Thor says "I wish I could trust you." And Loki seems affected by it.
During the battle against Malekith, Loki sees Kurse throw a Black Hole grenade at them. His first reaction is to push Jane aside even if it means he'll die.
Heartwarming in that he had no gain in saving her; it was like an instinctive reaction.
He also sheltered her when the Aether appeared to explode.
And then Thor saves Loki.
And most importantly of all; in spite of all his claims to have severed kinship with him like Odin has, Thor still loves Loki dearly in spite of himself.
And then Loki saves Thor.
There's also (possibly) the dialogue as Loki 'dies.' Made heartwarming as he has no reason to lie at this point, though it's Loki, so you can never really tell.
Thor: I will tell father you died with honor. Loki: ...I didn't do it for him.
At the end, when Loki is impersonating Odin on the throne, he genuinely, if he wanted, had the chance to turn the tables on Thor, and throw him in the dungeons for committing treason, and none would have questioned "Odin" on it. What does he do instead? He tells Thor he's proud of him, and lets him go. Sure, he's not really Odin, but despite finally being on top he chose not to completely screw his brother over when he had the chance, and even make him feel like he has the fatherly affection Loki never had.
Also, Thor did keep his promise to Loki by telling his "father" that Loki died like any honorable Asgardian.
Although as pointed out Loki is unable to take Mjolnir from Thor, so Odin not being able to take it away from him would be a tip off that something was wrong (if Thor was to be jailed wouldn't let him keep his power to escape with unless the jailer was foolish which Thor knows Odin is not). Letting Thor leave peacefully (and writing off him keeping his hammer as Odin being kind) was really the best option to get Thor out his hair without tipping him off. Granted he could have banished Thor, or just told him as Odin that he was disapointed in him but was letting him off because he saved the day so maybe Loki really wasn't just saying what he thought would be the best way to solve his problem. But it's really hard to tell with Loki, as again he might just have chosen the least suspicious way to excuse Thor keeping his hammer and going free which was to make Thor think Odin approved.
At the beginning of it, Darcy and Erik try to comfort Jane because Thor didn't come back.
In its way, the relationship between Malekith and Algrim is pretty sweet and caring. They're clearly fire-forged companions and while Algrim's self-sacrifice is ultimately for a pretty terrible cause, his total trust is pretty touching.
When celebrating the recent victory, Volstagg is shown surrounded by adoring children and holding a young girl on his lap. In the comics Volstagg is a proud father with many children, so it was nice to see them referencing that.
Hogun the (normally) Grim smiling happily when Thor tells him he should stay on Vanaheim for a while with his people.
Odin being a Shipper on Deck for Thor/Sif. It seems he approves of ladies being fierce warriors (makes sense, since Frigga is shown to be pretty badass herself).
The way Loki still calls Thor "brother" despite claiming that Odin is not his father and being still pretty messed/torn up by The Reveal.
Sif is strongly implied to be in love with Thor, who loves Jane. However, Sif never lets any jealousy influence her, and during the escape from Asgard, she is the one who gets Jane out of where she's being kept and later escorts her.