I don't read as much fanfiction these days as I used to, but these are the sites that I have found with a generally high signal-to-noise ratio, and which I do still frequent, at least occasionally. (However, "occasionally" may mean once every 6 months, so if you encounter a dead link, please email me and let me know.
(Note: Link updated June 2012. The original site seems to have been
abandoned by its webmaster, but the last updated content is still
available at Reocities.)
If you ship Jareth/Sarah, this is the place to go. Includes fan art, galleries, a message board, and a mailing list in addition to fanfiction.
An apparently author-restricted multi-fandom fanfic site, digital-quill hosts a good number of Labyrinth fics, including those by Scattered Logic, whose personal site (which I originally had linked here) seems to have vanished into the ether.
The biggest and the best of the Labyrinth fanfic archives. This was the repository for anything posted to the Labyrinth fanfiction mailing list, and while the original site has disappeared for unknown reasons, most of the content (including the stories) is still available from the Internet Wayback Machine archives, which are what I've linked above. So go and browse to your heart's content, but if you find something you really love, I would suggest saving it to your own computer so you'll still have a copy even if the archive eventually disappears as well.
Not a replacement for The Labyrinth Within The Labyrinth, but the archive here hosts a few of the same fics and seems to still be active, so that's something.
Given the nature of this fandom (and the severity of the ship wars I've seen go on) I think it might be prudent to state up front that I favor three ships, including (somewhat uncharacteristically for me) one slash-ship. These are:
The sites I recommend for fanfic, then, are biased toward those particular ships; if you happen to favor other pairings, you may not find a whole lot to interest you here. And, alas, one of the best sites out there, GryffindorTower.net, is now defunct, and I have not had the time to go looking for another Harry/Ginny archive.
I used to be a regular, or at least a regular lurker, on the Quill. I haven't had the time to keep up with it lately, but there's still a lot of good stuff in their archives, and their message board is a great place to find intelligent discussions and obscure trivia on all things HP.
Not an archive, but merely the single funniest HP fanfic I've ever read. If you're into HP and need a good laugh, go read this fic; you won't be sorry!
(Note: Link updated--the original site that this fic was hosted on seems to have vanished into the ether.)
(Note: Link updated May 2013)
Updates are a bit sporadic but there's still some good stuff here... I recommend anything written by Edith Crowe.
Part of the larger Classic Alliance of Beauty and the Beast site, this is a sizeable and regularly updated fanfic archive with collections of stories from some really excellent authors.
Warning: This is an adult-oriented site, not intended for minors. However, having said that, it's also a collection of the best romantic, amateur-written het erotica that I've encountered anywhere on the Internet--period. Highly recommended.
A nice archive of Han Solo/Princess Leia fanfiction. Adult-rated fics are marked as such.
The largest existing archive of Roxette fanfiction I'm aware of. (And, incidentally, the only place besides C&S where a story of mine has been posted. )
Can't get enough of Edmund Blackadder in his various incarnations? There's some very funny stuff here, including crossovers with just about every other fandom you can think of. The original site (like so many others--sigh) has vanished into the ether, but most of the content is still accessible from the Internet Wayback Machine archives--and as with the Labyrinth stuff, if you find something you really love, best save it to your own computer in case even this web version goes away in future.
A large general fansite for the animated series, with two fanfic archives, one general and one adult, the latter of which is password-protected.