Was having lunch with my better half and I was asked who were my favorite short story writers. Besides Borges, of course. Yes, she knows about my love for that writer as well. But, when I tried to think about my favorite short story writers, I had to add so many qualifications that it rendered such a list worthless. Same went for any specific books I wanted to pick. 
There has also been a change in me as writer. I'm writing more short stories than ever. And I'm trying to include as much as possible in my short stories as I can. Thus stories that seem to be crafted in an MFA workshop and are much ado about nothing, really rub me the wrong way.
So authors like Munro, Trevor, Adichie, GMG and DFW, though they write very well, and write some beautiful stories, don't fit the bill anymore. There are a few others with a more experimental vibe that I think I like, but wouldn't consider them as greats. In this realm I include the likes of Cortazar, and Bolano. Nevertheless, even if I wouldn't pick them, I recommend you check them out.
Here, then, is the list:
1) Borges, Borges, Borges. You can't go wrong with any book of his, though Ficciones is my favorite. (Also good are Aleph, and Universal History of Iniquity.)
2) Flannery O Connor's a Good Man is Hard to Find. Even though I don't like many who now write like her, she is the original and thus worthy of this list.
3) Solzhenitsyn is a surprise entry here. I bought this book off a bargain table and was in love. A great one to read, though keep a bottle of Scotch nearby. Apricot Jam & Other Stories.
4) Calvino's Difficult Loves has a large selection of his stories, but they're all worthwhile (see his Italian Folktales below).
5) Iraqi Christ by Blasim is a still the best book to come out of that dreadful war (yet). Fantastical and macabre, I'm not sure when I've been so riveted by short stories. Seriously some of the best stories out there, and you should read it as soon as you can.
(I think you can get a more comprehensive selection of his stories here).
There it is, what do you think? I should note that collections I love have not been included here. You should certainly consider the following: The Tongue's Blood does not Run Dry: Algerian Stories. And my personal favorite Italian Folktales. Read these, as they are nothing short of amazing.
I would also say that I've yet to read all that there is to be read and that the likes of Ursula and Vonnegut I have not explored enough to say yes or no to (even if I sense it will be a yes). And a final note is that I have not included the greats, like Chekhov or Gogol, but you should still read those too.
 For now I'll stay away from picking single stories, for I think Borges will come out dominating that list.
 I mentioned that in my classic literature post, where the propensity of a book to be reread is what marks it as a great book.
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