Star Trek IV: The Voyage Home/Heartwarming

After being "punished" with demotion at their trial, the crew are discussing what ship they've been assigned to, all agreeing that it'll be some clapped out old piece of rubbish... and then it's revealed to be a brand new U.S.S Enterprise...

Kirk: My friends... We've come home.

- Which the next movie revealed to be a brand new piece of rubbish.
- It's not rubbish! ...It was just put together by monkeys.
"Tell my mother... I feel fine."
- For the Trekkie audience, seeing Jane Wyatt make her appearance as Spock's Mom was heartwarming itself.
The scene in the hospital where McCoy gives the sick old lady on dialysis 23rd-century medicine... and a few scenes later, she's grown a new set of kidneys.
This exchange between our main trio:

Spock: Mister Scott cannot give me exact figures, Admiral. ...So I will make a guess.
Kirk: A guess? You, Spock? That's extraordinary!
Spock: I don't think he understands.
McCoy: No, Spock. He means that he feels safer about your 'guesses' than most other people's facts.
Spock: Then you're saying ...it is a compliment.
McCoy: It is.
Spock: Ah. Then I will try to make the best guess I can.

The waterfight at the end. Particularly when Kirk picks Spock up and throws him bodily into the water.
- Keep your eye on Spock in the scenes leading up to that. Is he... smiling? He might be, but he'll never tell!
It also has perhaps the only one that happens before the film even starts: it was released soon after the Challenger disaster, and the producers took it upon themselves to put the following at the beginning of the print: "Dedicated to the crew of the space shuttle Challenger, whose courageous spirit will live to the 23rd century and beyond."
Sarek HATED the idea of Spock joining Starfleet. But after all that, he pulls him aside at the end and admits he was in error.
- Really, the entire conversation is heartwarming in at least three different ways. Sarek shows his love for Spock, both unconditionally and with direct approval for his life choices; Kirk and the crew earn the respect of the reserved Vulcan (validating the entire intercultural-cooperation idea of the show, really); and Spock acknowledges his deep friendship with them. All with the typical reserve and formality of Vulcans, yet immensely powerful thanks to the performances of Mark Lenard and Leonard Nimoy.

Sarek: I am returning to Vulcan within the hour, I would like to take my leave of you.
Spock: It was most kind of you to make this effort.
Sarek: It was no effort. You are my son. Besides, I am most impressed with your performance in this...crisis.
Spock: Most kind.
Sarek: As I recall, I opposed your enlistment in Starfleet. It is possible that judgement was incorrect. Your associates are people of good character.
Spock: [matter-of-factly] They are my friends.
Sarek: Yes,of course.

And of course Trek's greatest Heartwarming Moment ever -- Kirk and company think they're being reassigned to the Excelsior, but just as Alexander Courage's classic fanfare plays we see...the brand new USS Enterprise, NCC-1701-A! Along with the classic quote, "My friends, we've come home." Trek fans weep and cheer every time at that scene.
- Except this troper can't watch it without laughing because she's seen the outtake of that scene, wherein there is a moment of silence and then Leonard Nimoy deadpans, "Quit touching my leg."
The scene where Kirk and the others talk about rescuing Chekov. They ask Spock what he thinks, and he agrees that they must save Chekov. Kirk asks, "Is that the logical thing to do, Spock?" Spock answers, "No, but it is the human thing to do." At that moment, Kirk and everyone else knew that Spock was truly back.
"Admiral! There be whales here!"