That's the single most unanswerable question for any writer, IMHO.
But I'll give it a shot.
Most of my fanfiction bunnies come straight out of canon. Even if it's not a missing scene or episode tag, normally my fic ideas sprout out of some unexplored moment, line of dialogue, silent look between characters, or a missed opportunity. (Respite; LOYALTY; The Nameless Seeker; Breathe For Me)
The others come out of something in my own heart, something I long to express. When something from one of my canon sources triggers that, a story is born. (The Longest Road; Statistical Ghosts)
A very few are what I call "meta fics." That's when I use a fic to explore something I've come to understand about a character or relationship in the source; when I write a fic rather than an essay. (Phantom Intelligence; Sua Sponte)
19 – When you have bunnies, do you sit down and start writing right away, or do you write down the idea for further use?
20 – Do you ever get bunnied from other people's stories or art in the same fandom?
21 – Sequels – Have you ever written a sequel to a fic you wrote, and if so, why, and if not, how do you feel about sequels?
22 – Have you ever participated in a fest or a Big Bang? If so, write about your favorite experience in relation to one. If not, are there any you've thought about doing? And if not, why not?
23 – When you post, where do you post to? Just your journal? Just an archive? Your own personal site?
24 – Betaing – How many betas do you like to use to make sure there aren't any major flaws in your fic? Do you have a Beta horror story or dream story?
25 – Music – Do you listen to music while you write? Do you make playlists to get into a certain "mood" to write your fic? Do you need noise in general? Or do you need it completely quiet?
26 – What is the oddest (or funnest) thing you've had to research for a fic?
27 – Where is your favorite place to write, and do you write by hand or on the computer?
28 – Have you ever collaborated with anyone else, whether writing together, or having an artist work on a piece about your fic?
29 – What is your current project or projects?
30 – Do you have a favorite fic you've written? What makes it your favorite? And don't forget to give us a link!