There are numerous freely-available online stories which I have very much enjoyed. Here is a partial list, updated at random intervals.
Nostalgebrist's story The Northern Caves captures online culture pre-social-media delightfully, and is also a great picture of obsession. His story Floornight is also fun, although less so.
Friendship is Optimal is of course the greatest collection of stories of all time, to which I contributed at least one story. (Vertas Vos etc.)
Scott Alexander's Unsong is good, although I haven't re-read it as much as I would have predicted. Beautiful language and sentiments, in some parts, but in other parts a single conceit stretched out too far. I like some of his other stories more; How Deep the Rabit Hole Goes, Universal Love, and so on.
QNTM's stories, both short fiction and longer, are great. The SCP set of stories is the best, in my opinion, followed by Ra and then Fine Structure last.
Greg Egan has many of his short stories free online.
Peter Watts Blindsight is also free online.
Alexander Wales wrote The Metropolitan Man, a retelling of Lex Luthor's conflict with Superman, as well as a delightful story of project management in the Star Wars universe.
Harry Potter and the Methods of Rationality. Edit: As of 2023/08/11, I no longer recommend this.