Zuko's three-season-long undaunted obsession with capturing Aang. Zuko even says that, for so long, his drive to capture Aang was his "inner fire." This is minutes after he and Aang dance together inside a fiery rainbow.
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 (yes, it needs its own one of those too) 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, the Foe Yay goes through the roof.
In the third season, there's an episode 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.
Zuko and Katara in "The Waterbending Scroll": "I'll save you from the pirates" indeed. Many a Zutarian, crazy and sane ones alike, have pointed to this scene as the one that officially launched the ship that would take over a large portion of the fandom, for better or worse. Many female viewers can't hear that line without wanting to squeal "You can save ME from the pirates, Zuzu!!!!!"
Three Words: North Pole Fight.
Azula and... just about everyone. Aang, Katara, Zuko (especiallyZuko, or as she calls him, "Zuzu"), Long Feng, Sokka, Toph, Suki... and she only gets this with Mai and Ty Leeafter they betray her. Really, Azula owns this trope.
For a man who supposedly hates the Avatar, Amon certainly has a lot of interesting interactions with her. During their first mutual meeting, he caresses Korra's face and leans in reaaaallll close, speaking to her in a low, seductive voice. He later performs a Villainous Rescue, saving her from Tarrlok, and as she runs there's a long slow-mo shot of their eyes meeting. He also seems to consider her a Worthy Opponent, warning his men not to underestimate her and setting out to capture her himself. Finally, in the Season Finale, after being unmasked, he throws one last look at Korra of debatable meaning before fleeing.
Tarrlok frequently pesters Korra to join his organization, even sending her very expensive gifts over and over "until you give in", and compliments her appearance at a dance. Then he kidnaps her, and while there is a legitimate reason given, there are certainly manyotherimplications.
Tarrlok makes a comment in episode 9 about how Korra ruined his plans and how now he's going to start a new life with Korra as his hostage.
You could also make a case for Mako and Tahno having some of this because of that sexy wink Mako sends Tahno during their Pro-Bending match. And whether it was intentional or not, the only other person who had gotten the sexy wink from Mako before Tahno was Mako's girlfriend Asami.