Something I don't normally read although I like the concept in parts. Taking your favourite characters and using them in ways that perhaps the author didn't think of (sometimes for good reason as they can skim close to pornographic at times.)
I had read a Doctor Who one once and while a pleasant to read it wasn't enough to make me a fan of fanfic.
However I did read one recently that was almost better than the original source material from whence it came. Called Wide Awake it takes the characters from Twilight (yes, I know but it made Meyers a multi-millionaire for some unfathomable, addictive reason and yes, I did read all of them - in one week no less) and twists them for grown ups.
Don't think Meyers would approve. Lots of her followers do though.