Below is a listing of websites where one can read classic and contemporary short stories at no cost. I will be updating the list periodically, so please feel free to make suggestions to the list.
The New Yorker
You can access some of the short stories published in the magazine for free on the website. Focuses mainly on established writers.
Words Without Borders
A wonderful resource for world literature, especially translated works.
Classic Short Stories
A good site for those looking for classic stories by the likes of Chekhov, etc
East of the Web
Features short stories in 9 genres.
Publishes short fiction and poems from a diverse group of writers.
Operated by Brooklyn Rail. Presents unpublished translations of short stories and book excerpts.
The Massachusetts Review
A quarterly magazine of literature, the arts and public affairs. A couple of published works are available for free on the website.
Tin House Magazine
Selected stories are available online
Literary magazine of the University of Florida. Selected stories available online.