I've written a few pieces of fanfic. Usually I write them because something in a story sparked a question that's never answered by the author. For example, in Laurell K. Hamilton's "Lunatic Cafe", there was a throwaway reference about Edward finding a witch to lift a curse. I wanted to know who the witch was. And, frankly, at the same time I wanted to explore a little bit about how a character could survive in that world and NOT be an uber-everything. So I wrote "Swan Song".
Then, because I liked the interplay between my OC and Edward, there was a follow-up. A third story stalled out, shortly after I realized I was writing it because people had asked me to write a story where my OC and Anita Blake met up. It wasn't the story I wanted to tell, so it died out.
I also don't consider it time wasted when I could spend it on my own stuff. For one thing, I myself do not have an actual well of creativity that can run dry. There's always something to do. Writing fanfic doesn't stop me from having ideas about my own writing. The time sink is the only thing that might apply, and it's irrelevant to me. I have no plans to publish, so it doesn't matter if it takes me two months or two years to finish a story. I love writing, I couldn't not write. I write a lot. But, although I have submitted a story or two (actually, two in the last fifteen years or so) for publishing, I don't really want to. I'm a writer, not an author. I write for the sheer love of it. Having to submit it to editing and deadlines and all the other crap that goes with being published would suck the joy out of it, for me. So I write, and fanfic in no way impinges on my ability to enjoy the hobby.
I don't read much fanfic because, as other people have said, the vast majority of it is terrible. Bad grammar, bad plotting, and don't even get me started on the horrible characterizations. "What if Jack and Daniel were blue, telepathic aliens?!" Then why use Jack and Daniel at all?
If I ever published my own work, I would let people write fanfic, assuming my lawyer or agent didn't have an aneurysm at the very notion. I dunno if she still handles it this way, but for awhile Mercedes Lackey used to permit fanfic IF the writers used an alternate timeline wherein a major character who had died in the "real" timeline managed instead to survive. Since most readers were upset he had died in the first place, that was fine.
I'd probably handle it in a similar fashion, if all the legal angles permitted. Make a drastic change, so that all fanfic is actually happening in an alternate universe.
I haven't yet written any Dresden Files fanfic, mostly 'cause Jim's doing a bang-up job of writing it himself.
If he leaves a big gaping hole in a story that bugs me no end, I suppose I'd end up scribbling twenty or so pages. But I have a feeling the Dresden Files RPG will give me all the room I need to tell whatever stories I want in that universe. Go MUSH!