I wrote Mr. Bradbury a fan letter back in college, and was thrilled when he wrote back with a personal response (who among you knew young Ray Bradbury once spent an afternoon trying to convince Walt Disney to run for mayor of Los Angeles?). Once I moved out to California, I got to hear him speak several times, and talk to him in person twice. He told me some wonderful stories about the priest at his wedding and how the Smithsonian once fired him "for being a smartass."
As for stories... if "all of them" isn't a fair answer, I'd probably pick...
"Usher 2" which got collected into The Martian Chronicles
"A Sound of Thunder"
"The Laurel and Hardy Love Affair"
I believe "McGillahee's Brat" is in Green Shadows, White Whale
, along with a lot of other stories about his time in Ireland doing Moby Dick
with John Huston. There's also a wonderful one called "The Terrible Conflagration Up at The Place," which is the most hysterical story of peasant rebellion you'll ever read. And also "Banshee," which Bradbury not-so-subtly claims he wrote one night instead of killing Huston.
"Pillar of Fire" is a novella-esque short story adapted from one of his stage plays. It's about the last dead man on Earth. It's brilliant.
And, of course, Fahrenheit 451
And, well... all the others.