I've done some fan fiction writing in my time, I will confess. I'm mainly written X-Files and Harry Potter stuff, though I did have a funny (at least to me) Underworld story going on that I actually kind of liked and am saddened that I can no longer find and never finished.
There are really two things I do with fan fic. One is that I'll get interested in a minor character who has some level of development but is not fleshed out enough to suit my obsessive standards, so I'll write some fiction stuff of my own to fill in the gaps. I don't think I've ever written a serious fan fiction about a major character simply because so much exists about them in the original source, I see no point in adding to it. I also tend not to mix invented and canon characters from any source. I have no idea why, it's just not an idea that appeals to me. I'll either write a completely original story or use all canon characters, with no overlap.
The other thing I do with fan fic is I really enjoy parody, satire, absurd irony, etc. I haven't really done much of that at Thar-- my character tends to be pretty serious, so my writing is too-- but comedy is a love of mine. In addition to the aforementioned Underworld story, I've written a couple of humorous (again, to me) X-Files fics, and a Harry Potter parody story.
I haven't done much actual posting of my fan fic. I usually just pass it around to my friends. I have posted three of my Harry Potter stories, though, and people have liked them, so I might do more at some point.
I don't tend to read a lot of fan fic, just because frankly so much of it is absolute garbage. I used to read a lot more of it, but I've lost the patience to sift through really lame stuff to find the gems. Those gems absolutely do exist, but I'm too cynical to be a gem hunter much these days.
One other thing that stands in the way of my fan fic reading is my lack of belief in and patience with teenage true love and romance. I just find stories about it rather pointless. The don't offend me, but I can't be bothered with stories that are solely driven by teenage crushes and affairs. So... that pretty much eliminates most of the Harry Potter fan fic oeuvre right off the bat for me.
I'd like to read some Firefly fiction, but I'm scared. So much has to go right with it, and there are so many great characters who have to be captured exactly. I just don't trust an amateur author to hit the right notes.
I tend to read fan fic, now, based on the recommendations of others rather than searching for it myself. And if you recommend it, I may or may not read it.
Why?
Because I am a stylistic snob. I am a preachy harpy with unreasonably high standards.
But that is who I am.
I'm glad to hear that. I really try, and I'm happy someone was convinced 
Just kidding... Yeah, I really try to make her hott. Again, I'm glad I'm convincing!
