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.

"365 Tomorrows"

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.