Eight authors answer the question above:
"I would be a liar, a hypocrite, or a fool -- and I'm not any of those -- to say that I don't write for the reader. I do. But for the reader who hears, who really will work at it, going behind what I seem to say. So I write for myself and that reader who will pay the dues." - Maya Angelou
"When I write, I aim my mind not to New York but toward a vague spot a little east of Kansas. I think of the books on the library shelves, without their jackets, years old, and a countryish teen-aged boy finding them, and having them speak to him. The reviews, the stacks in Brentano's, are just hurdles to get over, to place the books on that shelf." - John Updike
"I write for those women who do not speak, for those who do not have a voice because they were so terrified, because we are taught to respect fear more than ourselves. We've been taught that silence would save us, but it won't." - Audre Lord
"I write for the people I grew up with. I took extreme pains for my book to not be a native informant. Not: 'This is Dominican food. This is a Spanish word.' I trust my readers, even non-Spanish ones." - Junot Diaz
"When I write I try as far as possible to forget I'm writing it at all. I tell it down onto the page, as if I'm telling it to one person only, my best friend." - Michael Morpurgo
"Over the years I have come to realize that I write the book I want to read, the one I can't find anywhere." - Ann Patchett
"Any writer overwhelmingly honest about pleasing himself is almost sure to please others." - Marianne Moore
As for me, I write for my younger self...not so much the younger self I actually was, but the younger self I might have been had Fate shuffled her cards just a little differently: the one who didn't leave Pennsylvania, who didn't go to college, who didn't run fast enough and far enough to avoid replicating my mother's troubled, constricted life and who could barely have imagined the life I have now, its blessings and struggles alike. I write for her because I could have been her, oh so easily; and she -- and every young woman and young man like her -- deserves much better.
(In the old photo at the top of this post, snapped by Ellen Kushner in 2004, I'm at work on a folklore essay in Paris...a long, long way from the world I grew up in.)
"I want to write, partly at least, for the kind of reader I was when I was nineteen years old. I want to address that person because he or she is young enough that life is just beginning to seem a mystery which literature can address in surprising and pleasurable ways. When I was nineteen I began to read [William Faulkner's] Absalom, Absalom! slowly, slowly, page by patient page, since I was slightly dyslexic. I was working on the railroad, the Missouri-Pacific in Little Rock. I hadn’t been doing well in school, but I started reading. I don’t mean to say that reading altogether changed my life, but it certainly brought something into my life -- possibility -- that had not been there before."
That's it exactly.