Who owns a story? The writer? The reader? A writer of course can pull down any story at any time, but do they have the "right" to demand that every copy of the story be deleted? (From the Google cache, from the Internet Archive/Wayback Machine, from people's harddrives, etc.) Does a reader have the "right" to be able to find the story again? Do they have the "right" to download it, to pass it on to friends, to write their own fanfic based on it? Complex questions, I think.
I tend to think that, once a story is posted to the Internet, we lose control over what happens to it. It's out there, in the world, free to be read, reviewed, linked, copied, downloaded, fanficced. Why should we expect more control over our writings than traditionally published authors? A professional writer could never demand the return every publically available copy of a book. Once published, it's out there. Even if such a thing were possible, the story would live on, in the minds of the people who had read it.
Personally, I tend to think of a story as a collaboration between its writer and its readers. The writer creates the story, but it doesn't really come to life until someone else reads it. Perhaps this is a part of why we all adore reviews so much: a review is proof that someone read, that the story did indeed take on that life of its own. Maybe not the life we inteded for it, but a life all the same. (I think this is true for all stories, not just fanfic, although of course the feedback loop is more immediate in fandom.)
Anyway. Just my random thoughts on a Thursday evening. What do you all think?