I've never really been into fan fiction but a girl I used to work with was. I worked in a call centre at the time, and due to the weird shifts we used to work, seats were not assigned. This girl used to write Buffy the Vampire Slayer fan fiction. You would find short fiction, flash fiction, even chunks of longer stories on almost every computer in the centre. It was the most amazing writing, but there was lots of it.
They were not my type of stories, but I rarely got to read a lot of it. I suspect she would just write bits at a time while on break, so a lot of stuff was unfinished or never made it past the first draft stage.