Every writer started writing by being a reader. Sometimes as a voracious one. The mental stacks pile high, creaking under the weight of other people's characters, plots, worlds, languages, and adventures. A writer's lifetime of reading (and movies, TV, music, other art - wherever story can be found) becomes the fertile soil out of which her own stories sprout. My strong suspicion is that we're all of us writing fanfiction after a fashion - in this case, it's our stories that stand on the shoulders of giants. Though most of us have enough imagination to avoid cease and desist letters from publishers.
Granted, I do have a few stories in my files from my early days as a writer that are unabashed fanfic. They are complete copywrite violations. But I think they taught me voice. I could switch from writing a story in Anne McCaffrey's Pern and make it come close to matching her tone, then I could write a Star Trek story that I thought did a fine job of matching the tone of those characters. From there, you can deduce which worlds I'd write in if I could. Star Trek. Anne McCaffrey's Dragon Rider series. Anything Andre Norton - except The Witch World series. That one's not my fav. I'd totally write within the worlds of some of the MMORPGs out there in the world.
Since I'm not authorized to write officially in anyone else's playground, I simply acknowledge that I am paying homage to each of my literary heroes in what I write. I hope.