Listed roughly in order of descending preference.
“What's in Alaska?” (WYPBQP)
“I Could See the Smallest Things” (WWTA)
“Errand” (Elephant)
“The Student's Wife” (WYPBQP)
“Where I'm Calling From” (Cathedral)
“Whoever Was Using the Bed” (Elephant)
“What We Talk About When We Talk About Love” (WWTA)
“Pastoral” (Furious Seasons)
“Why Don't You Dance?” (WWTA)
“Cathedral” (Cathedral)
Notes:
WYPBQP = Will You Please Be Quiet, Please?
WWTA = What We Talk About When We Talk About Love
Notice that I did not include “A Small, Good Thing” (or its earlier incarnation, “The Bath”). That was intentional. When all I had read was the volume of his selected stories, it was one of my favorite Carver stories, but after reading the Library of America's perfect edition of his collected fiction last year and placing it in the context of his entire oeuvre, it dropped. (Though I still understand why so many people like it so much.)
The stories I selected were chosen for intricate and difficult to detail combinations of reasons. Carver like only a handful of truly gifted writers can cut to the heart of things. So while I think these ten stories are his best work for vague literary reasons, it is mostly because of their relation to my life that I specifically chose them. That's because lists like this are inherently subjective and I no longer have the compulsion to feign objectivity. Trust me; if you read only the ten stories on the list, you'd probably know more about me than about Carver himself.
A special note on the selection of “Why Don't You Dance?”: On the last day of my intro to lit class, my teacher, who was a huge Raymond Carver fan, read this story aloud to the class (instead of giving a final that he would have to grade, I suppose). I was 18. It was the second Carver story I'd read/heard (after the understandably ubiquitous “Cathedral”), but it was the first I fell in love with. For that reason, it remains a personal favorite.