Sokka's fantastic Moment Killer scene when he walks in on Aang and Katara's passionate kiss, and constantly referring to them as "oogie" afterwards, much to Katara's annoyance. Makes it better, the moment that he killed was originally the last scene of the series, and an extremely emotional one at that. Hilarious.
At the end of Part 1, Toph demonstrates to Katara exactly what "oogies" are.
Katara: (Hugs Aang) I just hate seeing you get like that, sweetie. Sokka: Um, Aang? Katara? You're giving me the oogies over here! Katara: Aargh! I am so sick of hearing about your stupid "oogies," Sokka! I don't even know what that means! Toph: I can explain. Give me your hand.'' Katara: (Gives Toph her hand) Toph: Gaaah... (Licks Katara's hand) Katara: ! Distant Reaction Shot: OOGIE!
Best part is how Toph apparently has Gene Simmons' tongue. Slides it riiight up Katara's ring finger.
Toph and the Gaang are watching a fireworks show while riding on Appa's back.
Toph: Hey, wanna know what fireworks are like for me? Close your eyes.
[Sokka does so]
Toph: [shouting in Sokka's ear]BOOM!!!
The three students at Toph's metalbending academy have some funny lines between them. "The city's probably doomed! We're probably doomed!" "I hate doom."
After Toph stops the Earth Kingdom rioters:
Sokka: Good thing you listened to her, folks! I was about to bust out Mr. Boomerang! Whack-a-pow!
Random Guy: Ooooh! "Mr. Boomerang"! Soooo scary!
(Sokka hits guy in the head with "Mr. Boomerang")
Plenty of moments when Sokka assists Toph's Metalbending class.
Sokka: You have to not only see the metal. But hear the metal. Taste the metal. And BE the metal!
The "Toph is blind" joke in Part 2:
Toph: Hey Sokka, am I doing this right? I'm trying to roll my eyes at you.
Iroh: First I cook balls of tapioca until they're soft and tender. Then I put them in tea, where they sit like little pearl-sized snacks at the bottom of each cup! Add a little milk and — ta da! — A revolution in tea is born!
Zuko: PTAH! What is that trying to sneak into my mouth?!
Aang: I've never had tea that's quite so... Chewy.
Iroh: I am a man ahead of my time.
The Running Gag in Part 3 that has everbody shocked at Sneers and Kori's relationship no matter what is going on at the time.
A reference to The Drill: Suki exclaims that it's dark in an underground tunnel, but Sokka quickly hushes her and says Toph's touchy about it.