Ginyu's realisation that all his men are dead. Really made Vegeta into more of a bastard for denying him that moment.
Dende healing Gohan while saying he's the only person he respects and can really talk to.
Even though it was Played for Laughs, Vegeta mentions that the Kanassans miraculously repopulated.
At the end of episode 27, Vegeta gives the "Super Saiyan" speech to Freeza for a third time, only now, he's talking about Goku. The incredibly pained delivery of the line as he's dying makes it all the more awesome.
Though Freeza does show more tolerance to the stronger of his minions. Seriously, in episode 28 he openly admits to himself that he misses Zarbon.
Goku's concern for Vegeta before and after Freeza kills him.
Vegeta's whole "keep being awesome" thing to reassure Team Three Stars victory against Freeza was kind of heartwarming since it meant he didn't intend to kill them.
Goku burying Vegeta after he died is surprisingly not turned into a joke, bar Freeza's snarky comments.
Gohan running up and giving his dad a hug after the battle.
The entire post-Spirit Bomb sequence, really.
Until Freeza came back, sadly.
Kami remarking that it's "easier than you think" to work with Mr. Popo. In spite of the fact that Popo is terror incarnate it's clear that he treats Kami a lot better than the other 'maggots'.
Popo ranks Kami above his own poop. For him, that is high praise indeed.
He identified himself as Goku's friend when he showed up at the hospital.
Despite how he's treated Krillin throughout the shows run, Goku's reason for going Super Saiyan here is still the anger he felt from Freeza killing his best friend.
Just like the source material, Goku still warns Freeza to get down to avoid his energy disk.
The Namekians killing Guru for lying to them about who caused the famine, resulting in the deaths of many, many Albino Namekians. They clearly showed their disgust and rage at Guru for tricking them to do such a thing.
And right before that. Dende asking for a hug was adorable, especially in contrast to his Creepy Child persona.
How about Dende actually showing that he loves Gohan?
The Turtle's birthday party in episode 31. His thank you was just so heartfelt.
King Cold is much more broken up about Freeza being murdered than in the original work.
He also in general seems to be a bit of a Doting Parent to Freeza, much to the later's embarrassment.
Piccolo's Big Damn Heroes moment against Freeza, accompanied by Gohan's gleeful "Mr. Piccolo!"
The revelation that the Capsule Corps jacket that Future Trunks wears once belonged to Bulma. A little creepy since it is a jacket she made to show off her midriff, but still heartwarming.
When Krillin crossed Goku's mind, the first thing he asked was if something happened to him. After Trunks attacked right the hell out of nowhere and Goku blocked it like it was nothing, he simply repeated the question. Nice to see Goku cares.
The entire conversation between Future Trunks and Goku is this. Future Trunks has already been through a lot, so it's kind of sweet that he finally gets the chance to talk with his childhood hero.
This exchange between Goku and Yamcha:
"You're my friend."
"Oh, Uh... thank you, man."
He did this after hearing Yamcha would commit suicide in the future after finding out Bulma was pregnant with Vegeta's child. Given that his reaction to Freeza showing up on Earth was "The dragon wouldn't be happy 'bout that one!", that means a lot.
Listen to Yamcha's reaction to it as well. After suffering as The Chew Toy for so long, he was legitimately touched.
Jump forward three years. Everyone's together just before the androids are set to appear. Bulma has a baby that everyone knows is Vegeta's. At worst, he seems annoyed that everyone assumes the kid couldn't possibly be his. Seems like Goku really helped back there.
Yamcha returns the favor by taking Goku to get medicine when he has a heart attack.
This exchange between Gohan and Goku after Goku accidentally slaps Chichi through the house walls and into a rock, which shows that, despite Goku's neglectful parenting, Gohan still cares about him and loves him:
"Oh my gosh!"
"The worst she can do is ground me, now run!"
Goku and Piccolo have formed a genuine friendship as of episode 34.
Shown big time in episode 36. For a few moments, Piccolo is clearly concerned for Goku during his heart attack.
After Dr. Gero attacks the city with his eye beams in episode 35, he brags that he just killed the entire population. Even Goku realizes that Gero couldn't have blasted anyone that was behind him, and is stopped from pointing this out by Piccolo. Piccolo, a former villain, showed concern for civilians.
Krillin tells Tien to get off of Yamcha's case after the latter forgets to provide important information. One Butt Monkey has to look out for another, it seems.
Episode 37 has Tien and Piccolo taking jabs at Vegeta's blandly named Big Bang Attack, acting like friends. Nail notes that Piccolo's not one to talk, being Mr. Special Beam Cannon, and they exchange suggested names until Nail makes one that Piccolo admits is pretty good.
It turns out Future!Trunks picked up his mentor's catchphrase.
It's small, but the way Yajirobe cares about the possibility of Baby!Trunks being hurt by the Androids when he, the baby, and Bulma are flying out to the battlefield. It's a stark contrast to Bulma's 'meh, whatever' attitude.
Yajirobe: <holding Baby!Trunks protectively> You do know your kid's in the plane, right!?
Bulma: Oh, he doesn't know what's going on.
Yajirobe: Yeah, I don't think that's the point!
In the Christmas Tree of Might special, Piccolo wishes Gohan a merry Christmas before being blown away. Brief, but touching.
At the end of the Bardock special, there is a montage of scenes from the original Dragon Ball series, showing Goku's youth to the main theme song, the actual end credits to the special albeit with CHA LA HEAD-CHA LA overlaid on it. Despite the silliness of the episode, it is nice seeing Bardock's sacrifice pay off.