To be blunt, the very idea of Fan Fiction makes me shiver. It’s walking over someone else’s dream, imposing your dreams onto that persons creation. I’ve never written Fan Fiction myself, and I’ve never knowingly read Fan Fiction in any form.
A few of you have just responded to my opening paragraph by thinking of the large body of works based on Star Trek, Star Wars, AD&D, and other such institutions. The vast majority of those works are not, in fact, Fan Fiction, they are Works for Hire commissioned by and with the full permission of the Copyright holders of those worlds.
This brings us to the confusion that often lies between separating Fan Fiction from inspiration. We are all inspired by something, and that inspiration will of necessity affect our future creations. I will take that a step further, without inspiration, there is no creation.
I will not go into the question of taking Fan Fiction a step further by engaging in plagiarism. At their core, the two are not synonymous, and should not be treated as such.