Yuletide is a 'rare fandoms' fanfiction exchange that has taken place every year since 2003. This year there are over 2000 stories in the exchange, exemplifying the sheer variety of fanfiction. No, it is not all about sex. No, it is not all about writing the ending
you wanted. No, it is not all unoriginal / smutty / badly-spelt / insulting to the original creators / silly.
Though obviously some of it is. Sturgeon's Law applies.
I'm recommending three works, for the sake of variety. There are quite a few others that I think are masterful: stories based on classics such as
Dracula and
We Have Always Lived in the Castle; on myths and fairy tales; on
Casablanca and
Singin' in the Rain; on, literally, hundreds of TV series and films that I have never heard of.
What these three works have in common, for me, is an obvious love of the original text; a sense of playfulness; a creative element that means they're not simple pastiche. Book-based fanfiction is different to fanfiction based on TV / film / music, in that there's an original voice, a canon prose style, to emulate. Not all book-based fanfiction does this: some does it so accurately that the stories read like works by the original author. (I'm not sure whether that's a good thing or not.) The two text-based works here do imitate the original pretty closely, but not slavishly.
Another thing they have in common: they sent me back to the original sources. As did quite a few others ...
( recommendations: Molesworth, The Lady's Not For Burning, Who Framed Roger Rabbit )