Pan helping Goku get himself under control when he was a Great Golden Ape.
Vegeta, while fighting against Super 17, remarks that he is an Earthling who carries the heart of the Saiyans.
Goten, Trunks, and Gohan buying Vegeta and Goku time to preform the fusion dance. The sight of it causes Goku to pause and watch on with a smile. Might be Dub Text but it's definitely heartwarming Dub Text! note In the Japanese version, Goku was snickering over the fact it was Vegeta who suggested fusion
Goku: *smirks and chuckles contently* Just soaking it all in, watching our sons fight together. It doesn't get any better than this.
Also a moment that doubles as Now I’ll protect you when SSJ 4 Goku is losing against Omega Shenron, both his sons charge into the battle, despite being massively outclassed and pull their father to safety—Gohan literally carrying him and Goten working as distraction.
The Funimation version of Grandma Pan's exchange with Puck in the series finale
Puck: You're related to Mr. Satan, the world's hero? And you're related to Goku too?
Pan: Yep. I've got more crazy relatives than I'll ever know what to do with... and they're all heroes.
The ending. Though GT in general had its ups and downs, the ending is nothing if not perfect!
Narrator: We had fun because Goku was there. He's cheerful, he's kind. That's the Goku everyone loves. And thus the story of Dragon Ball ends."
Despite what has been said about Goku being a bad or neglectful parent, he becomes absolutely LIVID when Eis Shenron has the audacity to beat up Pan.. Not only does he give a "The Reason You Suck" Speech, but he also starts a BRUTAL beat-down. Doubles as a Crowning Moment of Awesome.
During the final battle with Omega Shenron, when it appears that Goku has been killed, Vegeta charges at Omega while screaming "THIS IS FOR KAKAROT!"
A flashback to a family and friends day out on the beach, before Goku went off to train Uub. Goku, the guy who's always leaving his family behind to fight or train or both, actually said something contrary to that:
Chichi: It’s days like this that make all of the hard times we’ve been through seem worth it.
Goku: Well, I have to admit, I do miss all the fighting. *turns to look at Chichi, smiling* But here, I get to be with you guys!
Whether you like them or not, or even consider their existence canon, watching Goku Jr. and Vegeta Jr. is surprisingly adorable. The pair are polite to one another during their match (even if, true to his ancestor, Vegeta Jr. used a little Trash Talk early on), and seemed to genuinely enjoy themselves during the fight.
The song that plays in the Spanish dub at the end of the series, "Mi Corazón Encantado" is incredibly sweet. It is a nostalgia trip all the way through, as it is basically an anthem to all the wonderful memories you had as a child, and a loving sendoff to one of our childhood heroes.