I'm pretty sure I'm just doing this as an excuse to use that Sokka icon...
Do you have a "muse" character, that speaks to you more than others, or that tries to push their way in, even when the fic isn't about them? Who are they, and why did that character became your muse?
Avatar: the Last Airbender: Zuko. He's grouchy, angsty, and remarkably fun to fluster. Also, there are just so many places in canon that could have gone much, much worse; clearly, these potential stories must be written.
For a minor character, Ursa shows up in a large percentage of my stories. More recently, I think this is driven by the realization that the woman who married Ozai and killed Fire Lord Azulon was probably pretty scary. The desire to contrast that with Zuko's rose-tinted memories of her is very strong.
Young Justice: Wally. Characters that act, then think, tend to be really really good at getting themselves into the most interesting situations. This leads to all sorts of fun ideas. Also, when I'm trying to write the ensemble, he tends to talk a lot, which pushes him into the story.