The main reason I put this together is so that attendees at slashcon could have the beginnings of a common language. For that reason, I've tried to pick stories and vids which are widely recced and well regarded, but also readable to someone who doesn't know canon well. I've started right at the beginning with Kirk/Spock, and worked through to current fandoms. There's no need to read everything here; pick and choose as it pleases you. I've given some brief notes, so that you know why I've picked each story or songvid.
If people have other suggestions for well-known or influential stories, please leave links in comments. The more the merrier.
Star Trek: TOS
TREK Kirk/Spock, 'In Check' by K'Sal
TREK Kirk/Spock, 'Only Logical' by cimness
These two stories give a sense of the way Kirk and Spock are written in fanfiction, the way what we see on the screen is interpreted and certain tropes turn up again and again; in these particular stories you'll see what I mean in the way the authors use logic. This elaborating on canon tropes ends up building 'fanon' -- a widely accepted body of fan created tropes that are often repeated. The first and most famous such slash trope is demonstrated in the story below -- the pon farr dilemma.
TREK Kirk/Spock, 'Both Sides Now: Celebrating Kandy Fong' by Francesca Coppa (songvid)
This was the first songvid, made up of slides set to music.
TREK Kirk/Spock, 'Still Amok' and 'Coals of Fire' by Jat Sapphire
TREK Kirk/Spock, 'Closer' by T. Jonesy and Killa (songvid)
This story and songvid between them are a beautiful encapsulation of the fuck-or-die dilemma that turns up over and over in fanfiction. In this case it looks at Spock's pon farr. (Implied rape warning for the songvid.)
ETA: cimness, who was an active member of Trek fandom, has generously given further recs in comments. Her recs more accurately reflect what was popular back in the day, so are well worth a look.
PROS Bodie/Doyle, 'Army Games' by Sebastian
PROS No Pairing, 'Detachable Penis' by the Media Cannibals (songvid)
Another early fandom, this time in the cop/buddy genre. Much of what is now being produced in NCIS fandom and so on has roots in Pros and Starsky and Hutch.
HL Duncan/Methos, 'Hope Chest' by elynross
Interesting look at how a person can reinvent themselves, and some of the ways identity/sexuality/gender can be fluid. The fantastic elements of SF/F/H shows are often used to explore implications of character in slash fiction, as opposed to being the impetus for an action plot in canon.
ETA: Some of chaosmanor's fic has been opened up, here.
POPSLASH Kylie/Madonna, Britney/Madonna, Not Solidarity by Faithtastic
POPSLASH Justin/Lance As Lucid as Hell by Sandy
Two interesting stories which show some of the ways in which real-person fiction is examining celebrity and the way we create stories.
LOTRIPS Otto/Blanchett, 'Common Tongues' by cupidsbow
This is possibly my most famous Lotrips story, both because femslash is rare, and because it was well received (also rare for femslash).
dS Fraser/Kowalski, 'Eight Sessions' by cesperanza
dS Fraser/Kowalski, 'Ray Is Not Actually Graphing His Relationship With Fraser' by sprat
dS Fraser/Kowalski, 'How Ray Got His Groove Back' by Bone and Aristide
dS Fraser/Kowalski, 'Broadway Hotel' by resonant8
dS Fraser/Kowalski, 'Learn to Speak Canine in Seven Easy Steps' by etcetera_cat
In some ways, dueSouth fandom was a turning point, in that the canon invited meta-fiction in a way earlier shows mostly didn't. As a result, this is an inventive and funny fandom, and I've tried to represent that here, as well as give a sense of the range of approaches taken (oh, impossible task).
ANGEL Angel/Lindsay, 'Sea Change' by Yahtzee.
ANGEL Angel/Spike, 'Your Woman' by charmax (songvid)
ANGEL Various Pairings, 'Whatever' by Luminosity and sisabet (songvid)
An interesting fandom, because the relationship between Angel and Spike is strongly implied in canon (given that they are vampires) and confirmed by Whedon. The fanworks often explored various BDSM themes (often while still maintaining a sense of humour), and the power dynamic between human/vampire is often a key element.
SV Clark/Lex, 'Conflicts of Interest' by rageprufrock
SV Clark/Lex, 'That Old Schizophrenic Jealousy' by scribblinlenore
SV Clark/Lex, 'Three Impossible Things' by seperis
SV Clark/Lex, 'The Butterfly Effect' by The Spike
SV Clark/Lex, 'Mercy' by Koi (Dark themes warning)
SV Various Pairings, 'Drop Dead Gorgeous' by astolat (songvid)
SV Clark/Lex, 'Map of the Problematique' by raspberry_splat (songvid)
SV Clark/Lex, 'Without You I'm Nothing' by sisabet (songvid)
This was another powerhouse fandom, largely because of the huge amounts of conflicting canon. Many of the best stories used elements of the larger Superman canon not shown in Smallville, and considered both the godlike aspects of Clark's power, and the psychological damage done to Lex.
HP Harry/Draco, 'If You've a Ready Mind, by sarahtales
HP Harry/Snape, 'Maneater' by jarrow (songvid)
The largest fandom of all. I don't have anything to say about this one. There is too much. These recs give barely a taste, but most of fandom have read sarahtales, even if they aren't in HP.
ETA: kayleigh_jane has kindly linked to a 'best of' list in comments.
VOR Miles/Gregor, 'A Deeper Season' by sahiya and lightgetsin
A book fandom! There isn't really a substantive Vorkosigan fandom, but this is one of those fics that everyone reads. Awesome and clever.
HOUSE House/Wilson, 'Maryland' by astolat
HOUSE House/Wilson, 'Defensive Strategies' by milkshake_b
HOUSE House/Wilson, 'If We Shadows Have Offended' by mystictwilight (songvid)
I don't have much to say about these -- they are well done, and give a sense of some ways plot can be used to further slash. The songvid is a very clever constructed reality.
ANTH Canon/Fanon, 'The Corruption of Canon' by virtualinsomnia
ANTH Het/Slash, 'Het vs Slash' by pauraque
Fanfiction about fanfiction. :)
Stargate: Atlantis and SG1
This is the fandom I currently know best, so I've fleshed out the recs with some thematic stories, such as genderfuck and transformation, and also linked to some primers and other resources.
SG1 Jack/Daniel, Sam/Janet, 'Wormhole X-treme' by Lady G
SGA McKay/Sheppard, 'Freedom's Just Another Word For Nothing Left To Lose' by synechdochic
SGA No Pairing, 'This is How it Works' by Lim (songvid)
This story and songvid go together. This is probably the most famous story in SGA, and one of the most widely-read fanfiction stories to date.
SGA McKay/Sheppard, 'You're Pretty Good Looking (For a Girl)' by trinityofone
SGA McKay/Sheppard, 'Class: Insecta' by cupidsbow
SGA McKay/Sheppard, 'Place Your Hand' by mmmchelle
SGA McKay/Sehppard, 'Wide Open Ocean' by setissma
One of the many well-done alternate universes inspired by this fandom.
SGA McKay/Sheppard, 'Absolutely Cuckoo' by zoetrope (songvid)
A charming and funny constructed reality songvid.
Previous SGA rec lists I've put together include: A Primer for Reading SGA Fanfic, and A Genderfuck Reader in SGA.
lauredhel, you can find links to stories about disability here. Two stories are directly linked (they are stories which consider life with a disability in interesting ways), and two thematic masterlists are also linked, containing many more stories.
SPN Sam/Dean, 'Bad Blood' by astolat
The ethics of incest in stories is a current hot topic thanks to this fandom.
SCRUBS JD/Dr Cox, 'My Big Breakup' by iamsab
SCRUBS JD/Turk, 'My Gay Jungle Fever' by typicrobots
How to play with a very stylised canon.
The following are just a handful of posts about slash and fanfiction which will give some tiny feel for the way that fanfiction and commentary go hand in hand.
The Return of the Author: Contexts and Authorial Fallacies by Kristina Busse
How to Watch a Fanvid by Henry Jenkins
fanfic : pro-fic :: lazy: original? by astrogirl2
Authorial intent, derivative fiction, and literary criticism by carmarthen
What I'd like non-fans to know about fanfic by penknife
Anti Fanfic Bingo Card by ithiliana et al.
Continuum of Slash by linaerys
RPS: Another Perspective by hederahelix
rps characters are empty signifiers by lobelia321
Fandom and Male Privilege by cereta
Recommendations for further reading
ETA: As cimness pointed out in comments, the most representative multi-fandom slash resource is crack_van. It's a recommendation site in which many different volunteers rec stories in many different fandoms. For that reason, the quality is wildly variable, but it's hard to beat the number of fandoms represented, or the recognition of 'classics' from within those fandom.
You can find my multifandom rec site at rec_room (older stories), and on del.icio.us (for newer stories). Stories I think are particularly effective are Highly Recommended or given the Blue Ribbon.
I also maintain a list of other people's rec sites.
If it's meta you are looking for, you can find it on metafandom, or in my Memories under Slash Meta.