I need to rewatch the series, as it's been a few years since I last saw it. I remember greatly appreciating the patience the show had with its long form narrative; some things are set up, built to, and paid off seasons apart. But those moments hit so incredibly hard as a result.
I remember Aang going into his Avatar state (IIRC, in his search for the then-missing Appa) and being brought down to earth by the mother of all hugs from Katara. I cried at that scene.
I remember Zuko deflecting his father's lightning back at him in the throne room, gracefully and with a confidence that he'd spent the last season building up to, in one of the great moments of catharsis I've ever felt watching a show.
It's a show where nuanced characters make hard decisions in the heat of the moment that sometimes surprise themselves. When Azula's friends spontaneously betray her (I think it was Ty Lee), doing the right thing and surprising everyone, themselves included, in that moment, and having the consequences set Azula on a totally different trajectory for the rest of the show. That moment and the fall out were purely, 100% character driven.
Zuku's arc was covered in the OP, but my god what an arc it is. I've never rooted so hard for a character to turn the direction he did, and felt so good when it happened. The show had a patience to it that I just love.
Toph is awesome, of course, but I can't help but feel she didn't get the character arc her character deserved. The pieces were there with her background and family, but it didn't come together. Still, she was a delight.
Is that the hug I was talking about? It's my single favorite moment in the show. Just incredibly powerful, and IIRC done wordlessly. (Edit: yup,
this one.)
Well shit, someone is cutting onions or something...