Oh god the amount of fanfiction I wrote as a child. Uggg. Though admittingly I had a lot of fans and even still get notices about comments and people adding them to their favorites.
Not a fanfiction I wrote, but one I loved. It was a FAKE fanfiction. Now in this universe we had already established the two main characters were in love. They were together, all is well. However many fanfictions found online are mostly romance stories, or one shots that deal with the "inner emotions" of the character (or death fanfics... Or gay shipping... dammit). However this girl took the characters and ended up writing an entirely new plot for the characters, after the setting of the story. We already knew the two leads were together, and although there were romantic moments, it was all about the plot, NOT about them hooking up. She created a new villain with very good motives, made the current characters well rounded and kept them in character, and even answered some questions left by the main story.
I used to love fanfiction, but I hated how authors would con-strew already existing characters and pretty much made up a new character, only with the same name as the old. Example being many fan girls will morph a pre-existing character into a homosexual relationship with their mortal enemy. Not against homosexuality (the story I mentioned above is about two gay cops) however, that is NOT the character. That is NOT how they would act, and NOT the actions they would take. I suppose that's what it means to be a fanficiton, but I really enjoyed stories that were more dedicated to furthering the plots of the main along in their own creative fashion, rather then morphing and stretching already known characters into a Mary Sue, only said Mary Sue is a clone of said character.
As for previous question: Most popular stories I've written were probably "Bon and Bon" for Yami no Matsuei or "Second Shadow" for xxxHolic. Oh those days...