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.
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, said something that made me almost tear up.
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 or not you like them 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 Vegeta Jr. used a little Trash Talk early on), and seemed to genuinely enjoy themselves during the fight.