Joyland, Guernica, and most important The New Yorker. Unlike the other websites the New Yorker doesn't give away all of their short stories for free but still there's plenty that are free and great to read.
(The title is a little misleading. It should actually read, "Best of New Yorker Short Stories That Are Free on Their Website". Whatever though. So you won't be able to read the great Shirley Jackson's "The Lottery". Go find it in the bookstore and read it there. There are still some great short stories that have been written in the New Yorker recently that are completely free to read.*)
*Yes Kris I read the New Yorker.
Without further ado, here are some of the best New Yorker short stories. (Note: If you click on the author's name in the story, it will link to other articles/short stories they have written for the New Yorker. Stories that don't have a lock on them are the free one's.)
Symbols & Signs by Vladimir Nabokov: Along with Shirley Jackson's "The Lottery", "Symbols & Signs" is one of the classic short stories the New Yorker has published. This story is about a Russian couple buying a gift on Christmas for their insane son who is locked up in a mental institution.
I.D. by Joyce Carol Oates: Joyce Carol Oates is one of the most productive writers you'll ever see. Every year she is churning out novels, short stories, and book reviews. Her best shorty story in my opinion that appeared in the New Yorker is "I.D" the story of a kid who is pulled out of his Atlantic City classroom to talk to the police.
Deep-Holes by Alice Munro: Munro like Carol Oates, churns out short story after short story. Several of them have appeared in the New Yorker over the years and my personal favorite was "Deep-Holes". This story is about a young boy who falls into a hole during a picnic with his family. As he grows up he becomes sorta a weirdo who cuts off connections from his family but his mother wants to reconnect with him.
The Pura Principle by Junot Diaz: Diaz recently released a book of short connected stories. One of those stories is "The Pura Principle". Diaz's alter ego, Yunior, describes his relationship with an older teacher through the years.
Means of Suppressing Demonstrations by Shani Boianjiu: With all the Gaza Strip news lately you should read this story about Palestinians demonstrating by a Israeli checkpoint.
Love and Obstacles by Aleksandar Hemon: Hemon caught my attention with this heartbreaking personal history story about the death of his infant daughter. Hemon also writes short stories and his best in the New Yorker is "Love and Obstacles" about a emigrant in Chicago who goes to buy a refrigerator and meets local gun thugs.
Walter John Harmon by E.L. Doctorow: I loved Doctorow's book "The March" and I loved his story story "Walter John Harmon". This story is about a couple who join a cult in Kansas (think Branch Davidians) with the wife eventually leaving her husband for the cult leader (think David Koresh) and the husband is alright with it.
Literally by Antonya Nelson: Nelson has written many short stories over the years for the New Yorker but her most recent "Literally" has become my favorite. This is a layered story about two kids who's mother is murdered and their violent father who shows up.
Good People by David Foster Wallace: Weird fact, for all the great essays DFW wrote over the years he never wrote an essay for the New Yorker. You would think he would have but never did. DFW did though write several short stories for the magazine and my favorite is "Good People". This story is about a young Christian couple who have to decide whether or not to get an abortion for an unwanted pregnancy.
The God of Dark Laughter by Michael Chabon: This story is too dark and funny not to include it on the list. This story is about a clown from the circus who was murdered in Indiana and the subsequent investigation.
Magda Mandela and Raj, Bohemian by Hari Kunzru: Kunzru has only written two short stories for the New Yorker and they're both great reads. "Magda Mandela" is about a woman arrested in London who claims to be Nelson Mandela's daughter. "Raj, Bohemian" is about a hipster who feels betrayed by his hipster friends when they begin inserting product placements in their social lives. Seriously check out both of these stories.
Gunsmoke by Marisa Silver: Silver has also written quite a few short stories for the New Yorker but my personal favorite is "Gunsmoke". This short story is about a daughter who tries to convince her father to leave the house he's being evicted from before the police arrest him.
Bullfighting by Roddy Doyle: Doesn't the name Roddy Doyle sound like a race car driver's name? Anyway his story "Bullfighting" is about middle-age men who go to Spain to watch the Bullfights. This is like "The Sun Also Rises" if Jake Barnes was a middle-aged man.
The Porn Critic by Jonathon Lethem: I'm not the biggest Lethem fan but his short story "The Porn Critic" is a fun read. This story is about a hedonistic adult store operator trying to fall in love.
All Aunt Hagar's Children by Edward P. Jones: A story about an African American man just back from the Korean War vet who wants to go to Alaska to pan for gold but must first investigate the murder of his cousin. Oh yeah he also has dreams about a white woman who he saw die.
What Kind of Furniture Would Jesus Pick? by Annie Proulx: "Brokeback Mountain" orginally appeared in the New Yorker but that story isn't free. Instead you'll have to settle for Proulx "What Kind of Furniture Would Jesus Pick?". This is a story about the last cowboy on a ranch that is dying.
Red from Green by Maile Meloy: Story about a woman who goes camping with her father and a oddball group of people.
These are just some of the great short stories to appear in the New Yorker. I've bookmarked other great stories and if you wish to read some of them contact me at @KSJ49 on Twitter and I'll link them to you.