I was actually interested in this question about ten years ago, because around the same time that I started publishing short stories, I also tried my hand at writing for fanzines. If you check my Nonfiction Bibliography, you'll see that I published a few articles in fanzines such as Mimosa and Proper Boskonian. You'll also notice that I really need to update the bibliography, as a few years ago Nomi and I published two issues of our own fanzine, Burstzine, which you can dowload as PDFs if you click on the link.
Now, when I started publishing articles in fanzines in the mid- to late 1990s, I was pleasantly surprised to discover that my fan writing was striking as much of a chord with readers as my pro writing. Although I never got nominated for a Best Fan Writer Hugo, I did discover my name popping up on the "bubbling under" list, the list of nominees who missed making the top five. After a few years, though, my name stopped showing up on that list, because I spent more of my time publishing stories than fan writing.
But now that the floodgates are opening up...
In our current Internet world, everybody tends to become a self-promoter. I've noticed that reaction to such self-promotion tends to go in waves. It's considered gauche when the first person does it, then others slowly join in, until finally it becomes pretty much accepted across the board.
(Quick digression: This story may be apocryphal, but I heard that once upon a time no one ever campaigned for a Nebula Award. Then, one day, one of the nominees chose to mail out copies of their story to all SFWA members. A backlash ensued, and people deliberately voted against the story because of what appeared to be campaigning. But within a few years, everyone was mailing stories out to members, and today, stories are provided for members electronically and almost no one thinks the worse of anyone for it.)
Anyway, when I saw that other writers had begun discussing their blogging in the context of this award, I decided that it would not be at all inappropriate for me to do so as well. My voice will most likely get lost in the cacophony anyway.
So am I eligible to be nominated for the Best Fan Writer Hugo? I would say yes.
Do I want to be nominated? Let's just say that I wouldn't turn it down if it happened.
If you want to give my writings due consideration, you can click on the link for the MABFAN's Musings: 2006 calendar. (Remember that the 2007 Hugo Awards are supposed to be for work published in 2006.) If you want to read the posts I specifically tagged with the phrase "science-fiction," you can click on the provided link, and page back to see what I wrote last year. But since fan writing can really be on any topic, you might also want to re-read the stuff I filed under "writing-advice," which includes all my "roberts-rules" posts. Or see what I had to say in the world of "science"
I should also note that the essay I wrote for the book "Boarding the Enterprise: Transporters, Tribbles and the Vulcan Death Grip in Gene Roddenberry's Star Trek" edited by David Gerrold and Robert J. Sawyer (BenBella Books, August 2006), could also be considered fan writing. So if you've read that essay, you can feel free to take that into consideration as well. (And, hey, that book is eligible under Best Related Book if you're so inclined.)
And, finally, a reward for anyone who has read this far. Last year I published only one story, "Redemption in the Quantum Foam," which appeared in the "Space Cadets" anthology published by last year's Worldcon. The book was a limited edition, and it still doesn't appear as if it's being sold in great quantities on line or in bookstores. (Amazon lists only one copy available, from an outside seller.) I doubt that the story is Hugo-worthy anyway, but if you want a free electronic copy, email me at firstname.lastname@example.org and I'll send you one for your consideration.