Stories focused on the family and the friendly relationships of the cast. Plot-focused stories or light day-in-the-life stories. Pretty much anything that isn't focused on romance.
MSTtings of The Rangers of NIMH and The Rangers of NIMH II by Håkan Svensson & Kevin A. Pezzano, originals by David Gonterman (first story co-written with Paul Lapansee)
One of the classic MSTings, this follows Mike and the 'bots on their journey through the "magical" land of The Eye of Argon. Some of its lines have even made their way to being page quotes on this very wiki — a true sign of a brilliant fic. Even better yet, it actually turned this troper on toward the original TV show. She'd never watched an episode of the show prior to reading this fic, but after seeing it linked here on TV Tropes, she read it — and immediately couldn't snap up enough of the original show. Now there's a recommendation!
A MSTing of the Chick Tract "Dark Dungeons," which is Jack Chick's condemnation of Tabletop Games ("Dark Dungeons" is an Fictional Counterpart for Dungeons & Dragons). The website is set up like a Sci Fi Channel episode of the show, complete with a MIDI and animated GIF version of the opening sequence. The jokes not only go after Chick's bashing of things he doesn't understand but also make plenty of references to geek and tabletop RPG culture.
A collection of short, script-styled fanfics that bridge off from canon some point before the end of Season 6 (TV's Frank is around in the first short). The general synopsis is that Joel has been returned to the SOL and, after Dr. F cuts them loose, they drift off into deep space. Joel and Mike get frozen and the bots switch off eventually. Four hundred years later, they are found by a "Dominion" (i.e., Starfleet) ship, and their propulsion systems are fixed to they can cruise around the universe. After some time traveling wackiness, the crew crash lands in China...where they fall into the Spring of the Drowned Girl. Yes, all of them.
Apart from a few canon errors (Mike never worked for Gizmonic; he was a temp) and repeated usage of "Gizmonics", it's a pretty good read with some great humor and the characters are written in-character. Well, one could make arguments for Cambot...
A story set in Season 5 right after Mike's ascendancy to the Satellite of Love, it details Joel's adventures following his escape, including the consequences of accidentally defrauding Gizmonic Institute of $14.78, foiling Dr. Forrester's sinister and quite outlandish plot to take over the world (of course!) and building yet another robot companion to assist him in all the chaos. Very much in the spirit of the show, quite meta, and hilarious all around. Some knowledge of the early series is handy for getting all the jokes, but not needed to understand the story.
For a time, the link led to Molossia's website. It shouldn't anymore, but keep we should keep our eyes out for some kind of conspiracy. Bet Dr. F's trying to erase the evidence...
Set after the end of the series, Mike's apartment is launched into space by Doctor Erdhart, who has decided to continue the experiment and make Mike Nelson and his robot pals torture themselves with the worst Fan Fiction he can find. Feels just like the show, complete with host segments during the fic, definitely worth a read for both hardcore MSTies and newbies alike.
Wario Barker: Easily the best thing I've read in some time, despite remaining dormant for over 18 months (although if you're going to never update this again, the end of Chapter 12/Episode 10 is a pretty good way to go). Highly recommended.
Set during the final episode of the series, between the moment the SOL crashes on earth and the final scene with Mike and the bots in their new apartment. Shows how they survive the crash, get in trouble with Gizmonic Institue, and meet both Joel and Dr. Erdhart again.
Stories focused on the romantic relationships between the cast.
Sadly, none listed here yet, although there's a growing bit of it out there — check out Livejournal's MST3KSlash webpage, or just Google "MST 3 K slashfic". Joel/Mike is the most frequent pairing, known as "JOIKE" after Gypsy's sweater during the episode mocking the Mexican flick Santa Claus.