some more stories for the list:
Eliezer Yudkowsky's free online short stories
Not all of this is hard sci-fi, but most of it is.
Lots of free stories by Cory Doctorow, most notably Down and Out in the Magic Kingdom
These stories have varying degrees of hardness in the sci-fi
"After Life", by Simon Gordon
An awesome story about a Singularity started by an uploaded human mind. Reasonably hard sci-fi.
and here are some stories that don't qualify as hard sci-fi, that you might like anyway:
"I have no mouth and I must scream", by Harlan Ellison
A very nasty story. A standard example of a "hyperexistential disaster" caused by an Unfriendly AI. Technically not hard sci-fi.
"Postsingular", by Rudy Rucker
This novel provides a convenient introduction to several transhumanist concepts, though the plot itself seems to be deliberately anti-transhumanist.
"Understand", by Ted Chiang
An entertaining story about "hacking" the human mind. Demonstrates the risks of a dangerously selfish person being the first to succeed at this. not really "hard" sci-fi at all.
"I don't know, Timmy, being God is a big responsibility", by Sam Hughes
An interesting story about some of the unexpected anthropic dangers of simulating entire universes, with an "infinitely powerful" computer.
"They're Made Out Of Meat", by Terry Bisson
An amusing short story illustrating the silliness of "carbon chauvinism"
that story about the clinic seed, by Keith Henson, Part 1 Part 2 Part 3 Part 4
A story about what might happen to primitive human cultures, after the Singularity.
Only some of these stories qualify as hard sci-fi
Oh, and of course there's the massive collection of sci-fi stories in the Baen Free Library. I haven't even begun reading through this yet.
"that story about the clinic seed" gets my recommendation, "I don't know, Timmy, being God is a big responsibility" is fun, as is "They're Made Out of Meat", but my favorites have to be Doctorow's stuff. "Rapture of the Nerds" gets incredibly Posthumanistic at points.
Transhumanism and Hard Sci-fi category at FictionPress.com
Lots and lots of sci-fi at FictionPress in general (no hardness guarantees made)
My sci-fi short stories, in varying degrees of hardness and in two categories. (T) marks significant transhumanist themes.
Fragments of frozen time:
Childhood's End Even after nine years, people still stare at us.
Cthulhupunk With his mad, half-unseeing eyes, Calinob Dis stared into the eternity.
In a Billion Years Their embrace is wordless, simultaneously physical and mental. (T)
The Chamber of Sounds I stand here, in my small closet, locked away from all other life.
To Live and Die for the God-Emperor The party in the Menovian asteroid belt has been going on non-stop for ten millennia now.
Stories:
Colonization Humanity is standing at a crossroads, at a time when the galaxy still remains ready for the taking.
Cryoshift A rebirth. (T)
Union Two lovers, machine-mediated telepathy, and the consequences. (T)
The Ware Tetralogy: Free SciFi Download
Between 1982 and 2000, Rudy Rucker wrote a series of four sci-fi novels that formed The Ware Tetralogy. The first two books in the series – Software and Wetware – won the Philip K. Dick Award for best novel. Later Freeware and Realware followed. This summer, Prime Books republished the tetralogy in one big volume, complete with an introduction by William Gibson that calls Rucker “a natural-born American street surrealist” or, more simply, one sui generis dude. And now the even better part: Rucker (who happens to be the great-great-great-grandson of Hegel) has released The Ware Tetralogy under a Creative Commons license, and you can download the full text for free in PDF and RTF formats. In total, the collection runs 800+ pages. For more information on the book and the free download, visit here. And don’t forget to donate to the Creative Commons Legion of Superheroes fundraising campaign.
Here's one of mine:
Not actually fan fiction, but inspired by two existing works many readers will recognize.
Does Schlock Mercenary count as Hard Scifi? What about Freefall? They've both got FTL travel, and the former has other fairly miraculous technologies (like the matter annihilation plants and artificial gravity systems intimately related to them), but they're well thought out with the rational implications of them seen and discussed.
I deleted one of the links. I mistakenly copied it from another list. Just delete the story by Ian R MacLeod if you've saved it.
I posted a link to this on reddit/r/scifi, reddit brought back this list in return:
Novels
Blindsight, Peter Watts
Ventus, Karl Schroeder
Crisis in Zefra, Karl Schroeder
Accelerando, Charles Stross
The Lifecycle of Software Objects, Ted Chiang
Short Stories
The Island, Peter Watts
The Things, Peter Watts
Short Stories by Peter Watts
Divided by Infinity, Robert Charles Wilson
Crystal Nights, Greg Egan
Short Stories by Greg Egan
The Finale of the Ultimate Meta Mega Crossover
Three Worlds Collide