Among the regular flavors of Zutara: Katara being kidnapped by Zukonote This was reversed by Enslaved, Katara's season three hatred for Zuko revealing itself to be sexual attraction, Zuko siding with Team Avatar in the Crystal Catacombs, Mai dying in childbirth and Katara comforting Zuko, and Mai and/or Aang turning evil. Katara usually ends up as Zuko's queen in these stories (the flipside of this, Zuko renouncing his title and living at the South Pole with Katara, is rare).
The Dangerous Ladies, or just Azula herself, kidnapping or capturing Sokka, or they're stranded alone together in the wilderness, and they come to bond romantically.
If a fic set after the war isn't based around the gargantuan amount of reconstruction and peacekeeping required throughout the world, then it will casually mention it as if the reader should already know. Indeed, despite the series as a whole ultimately falling on the idealistic side of the sliding scale nearly every fan reaches the conclusion that no, it isn't going to be that easy.
This, of course, became canon in the follow up comic series "The Promise" which shows problems include Fire Nation colonists refusing to move, lingering racism between nations and Zuko's own doubts about his leadership.
When an OC from the real world falls into the world of avatar, one of two things are certain to happen: either she (it's almost always a she) will end up on Zuko's ship, join his mission, and fall in love with him or she'll end up joining the Gaang on their adventure.
Quite a few people like to write about how Zuko managed to find his mother.