I wouldn't say he was a terrible writer, but a writer who didn't know his own strengths. Honestly, check out the writing style of 'The Thing on the Doorstep', the ole Gent from Providence was almost starting to write like Hemingway when he died. If he had lived longer, we might have seen Lovecraft become the great writer he clearly could have been.
Here's an obscure one: "The Bamboo Trap" by Robert S. Lemmon. Also, "Leiningen Versus the Ants" by Carl Stephenson. "Blowups Happen" by Robert A. Heinlein. "Microcosmic God" by Theodore Sturgeon. "The Nine Billion Names of God" by Arthur C. Clarke. I'd like to echo "The Short Happy Life of Francis Macomber" by Ernest Hemingway. "The Tell-Tale Heart" and "The Fall of the House of Usher" by Poe. "Hero" by Joe Haldeman. "Flowers for Algernon" by Daniel Keyes. (That one totally wrecked me.)
I've read and reread this one over the last few years: http://www.newyorker.com/magazine/2010/02/15/foster . It's gorgeous.
A lot of my favorites (particularly, those by Hemingway and Hawthorne) have already been mentioned. Others: Jack London's "To Build a Fire" should also be on this list. ZZ Packer's "Drinking Coffee Elsewhere" occupies a special place in my heart. Another Hemingway "The Killers"--Decent Dialogue and really demonstrates certain aspects of Papa's style. Faulkner's "Barn Burning" (one of my favorite opening lines) Lovecraft's "The Thing on the Doorstep" (another favorite opening line--just noticed Lemex had already nodded to this one--oh well) Melville's "Bartleby" and "Billy Budd, Sailor" are also favorites. Neil Gaiman's "Other People" is rather fun.
Charlotte Perkins' Yellow Wallpaper. It's disturbing and harrowing, and left me feeling pretty anxious, but I actually like it when fiction has a notable effect on me, be it positive or negative.
"A Pail of Air" by Fritz Leiber. I remember this story, having first read it way back in elementary school. I think it was one of the stories in our literature anthology...I must've been 4th grade, give or take.
Roald Dahl's, Lamb to the Slaughter has always stuck with me. I just couldn't believe that he wrote it, it feels so old, like it should have always been there. And so unbelievably clever too!
The Emperor series by Conn Iggulden. Was the first series that really got me into reading. Must have read the whole series four or five times.
Air Raid by John Varley. I read it in Omni magazine back in the 1980s. The movie (Millennium) sucked big time, though. I haven't read the novel that he wrote based on the short. In fact, I didn't even know it existed until I Googled Air Raid just now (because I forgot the author's name)
The Queen of Spades - Pushkin Super-Frog saves Tokyo, Birthday-Girl, Blind Willow, Sleeping Woman - Murakami Metamorphosis, Before the Law - Kafka The Circular Ruins, The Library of Babel, The Garden of Forking Paths - Borges The Snows of Kilimanjaro - Hemingway and this one: http://www.newyorker.com/magazine/2013/11/18/guy-walks-into-a-bar
Cannibalism in the Cars by Mark Twain. I read this short story in a short story collection by Joyce Oates and it has stuck with me every since. Great story...
Popular Mechanics by Ray Carver. To Serve Man by Damon Knight Mouse-Kitty by Rick Norwood Greasy Lake by T. Coraghesson Boyle Giselle's Admirer, Marble Girl, Marco the Molasses Man all by Richard Lunn
I have Kindle Unlimited now and just got some free stories that were published within the last 30 days and damn there are some good up and coming sci-fi short story writers out there!
For me Burning Chrome by William Gibson. Perfectly creates this sad, grey world with characters who are just kinda getting by. Once I made my girlfriend listen to an audio version of it and she described it as 'the most depressing thing I've ever heard'. I think Gibson would have been proud of that.
In my personal view, currently now, a superb storyteller can be found in Roald Dahl. My top short stories are: Mrs. Bixby and the Colonel's coat, Parson's pleasure, the great automatic grammatizator(highly recommended for aspiring writers, you'll amaze yourselves) and the Way up to Heaven
Stories that haven't been named already: Eumenides in the Fourth Floor Lavatory (Orson Scott Card) Desiree's Baby (Kate Chopin) Aud's Troll Story (Nicola Griffith) A Retrieved Reformation (O. Henry) In the Penal Colony (Franz Kafka) Shall the Dust Praise Thee? (Damon Knight) William Wilson (Edgar Allan Poe) Can These Bones Live? (Ted Reynolds) The Fallen Country (S.P. Somtow) We Don't Know Why (Nancy Springer) Lather and Nothing Else (Hernando Tellez)
"The last question" by Asimov. I once read an interview, where he told that people would often ask him about names of stories stuck in their minds but with forgotten titles. It was almost always this one. It got so that he answered without even asking about the content of the story and people would think him a mind-reader I must confess, I also forget the name again and again. Have to look it up every single time but this story is stuck and won't ever go away *sigh*
Jorge Luis Borges: "Tlon, Uqbar, Orbis Tertius" Actually, also by him: "The Library of Babel", "The Garden of Forking Paths". Really, pretty much all of them. He's up there with Chandler and Kafka, in my book, as a master of the form.
From way back when I in grade school (4th or 5th grade) I read "A Pail of Air" by Fritz Leiber. It's about a young boy and his family trying to survive after the Earth has been torn away from the sun, and the different elements/contents of the atmosphere have frozen in layers. His job is to get a frozen pail of air on a regular basis so that it can thaw and provide oxygen for his family. While out getting air, in an adjoining skyscraper, in a window he sees what he thinks is another person... A short story in more recent times was "The Short Bus" by Marshela Rockwell. It's an inspiring story about mentally handicapped children, focusing on one boy, trying to survive at school. And while they're on their school bus, all of the children are 'normal' and can converse. A sad even is happening in that one of the children's family is moving...and she won't be able to ride the bus anymore.