Zuko's three-season-long undaunted obsession with capturing Aang, thinking of nothing but him and frequently dropping everything to chase him, even if it would make things worse for him in the long run. Zuko outright says that, until his Heel-Face Turn, his drive to capture Aang was his "inner fire". This is minutes after he and Aang dance together inside a fiery rainbow.
In "The Blue Spirit", Zuko risks imprisonment or death to rescue Aang from Zhao's clutches. Afterwards Aang thinks they could be friends, reluctantly running away when Zuko attacks him. Aang brings this up in season 3 to argue why Zuko should be a part of their group, only for Katara to retort that Zuko probably only wanted Aang for himself.
Back in the first season, this conversation between Katara and Aang at the end of episode 15:
Katara: Aang! How'd you get that? (referring to the necklace Zuko stole from her) Aang: Zuko asked me to be sure I got it to you. Katara: Oh, that's so sweet of Zuko. Could you give him a kiss for me when you see him?
One bit that is noted on Avatar's Ho Yay page is that when Aang is having nightmares in season 3, Zuko appears shirtless in his dreams. This would be suggestive enough on its own, but when you remember that all of Zuko's Shirtless Scenes happened when Aang was not present, and consequently Aang has never actually seen Zuko shirtless.
Parodied in the Rifftrax of the film where Kevin Murphy [as Zuko] quips, "I have no time to think about girls when I'm obsessing over a 12-year-old boy. Wait, that came out wrong."
The third season episode "The Avatar and the Firelord" is about Aang's and Zuko's predecessors, Avatar Roku and Fire Lord Sozin, who started out as friends... best friends! All their lives! Who shared a birthday! And Sozin didn't get married and have kids until way late. Come on. You just know he only wanted to conquer the world to win his true love Roku back. Too bad Roku was straight, really. So much tragedy could have been averted. If you think about, this makes the fact that they now share descendants hilarious.
And by Sozin getting married way late, we mean that he didn't get married and have his son Azulon until he was about 82, according to Avatar Wikia. You know he was just holding out for Roku to return his love but eventually decided he needed an heir.
In "The Waterbending Scroll", Zuko having Katara tied to a pole and huskily whispering in her ear "I'll save you from the pirates" is certainly... something.
Zuko finds Katara's necklace and uses it to hunt down the Gaang, eventually using it in the above episode as a bargaining chip. A later episode reveals that it's a Water Tribe betrothal necklace.
The North Pole fight was the most emotionally charged in the series up to that point, with the Foe Yay partly Zuko/Aang (they're essentially fighting over who gets to have Aang) and mostly Zuko/Katara.
Azula and Zuko, to almost Mind Game Ship levels. When she isn't playfully teasing Zuko (or "Zuzu" as she calls him) she's exploiting his fears and insecurities for her own benefit, somehow making "brother" sound more erotic than Liquid Snake did. As foreshadowed in a dream where Azula (represented by a blue dragon) practically seduces Zuko, Azula's We Can Rule Together spiel in "Crossroads of Destiny" much more closely resembles a Femme Fatale trying to drag The Hero into villainy than siblings plotting conquest. Reached it's peak in "The Awakening", where Zuko decides the best time to confront Azula is in her bedroom while she's sleeping, and Azula decides the best way to deflect his accusations is to get way too close to him for comfort while wearing nothing but a robe.
Azula has regular Ho Yay with Mai and Ty Lee, but after they betray her it transforms into Foe Yay during her Villainous Breakdown. "They'll all betray me in the end, just like Mai and Ty Lee did..."
Azula fights Suki, and it's revealed several episodes later Azula defeated her and took her clothes. The next time she's mentioned Azula taunts Sokka (Suki's boyfriend) that Suki is her "favourite prisoner" and talked about how Sokka would rescue her, before eventually giving up. Gee, I wonder what that could be implying?
Aang, Sokka and Toph bust into where they think Ozai is hiding, only to find Azula waiting for them. They demand she tell them where Ozai is, and Azula quips "Am I not good enough for you? You're hurting my feelings."
The really funny thing about Azula's Foe Yay is that it seems to be almost unintentional on her part- the one time she actually tries to seduce someone, it fails spectacularly. We Can Rule Together, coupled with flaming hands and a psychotic smirk, apparently doesn't make for a good pick-up line... unless you're using it on your older brother.