Some of Bradbury's earliest work on radio was for Suspense, one of the greatest of all OTR programs. Bradbury's work appeared occasionally over the 20 year span of Suspense; he even wrote the introduction to the series episode log I own! My first recommendation is "Riabouchinska," from November 13, 1947. I've heard some people aren't fond of this adaptation, but I think it's very good and I prefer it over the television versions which appeared on Alfred Hitchcock Presents and Ray Bradbury Theater. I think I prefer it because this version is told with a narrator, thus leaving in much of Bradbury's original text.
On November 25, 1948, Suspense adapted "the Screaming Woman." It deviates from the original ending, but it's still quite good.
The Suspense adaptation of "the Whole Town's Sleeping" from June 14, 1955 is pretty creepy; again, it uses a narrator, retaining a very Bradburian voice.
Suspense didn't tell many science fiction stories, but they did a terrific job with "Kaleidoscope" on July 12, 1955. I heard this episode again about two weeks ago; I'd been napping while OTR played on my computer and gradually woke up to "Kaleidoscope," which was very disorienting - it was as though I were a character in the drama being addressed by the men drifting helplessly in space.
Suspense's sister program Escape only adapted a little Bradbury, but they did a great job with their July 25, 1951 version of "the Earthmen," one of the Martian Chronicles stories.
The CBS Radio Workshop brought in Bradbury himself on February 2, 1956 to introduce adaptations of two stories, one from Dandelion Wine: "Season of Disbelief" and "Hail and Farewell."
Finally, there's the many adaptations which appeared on Dimension X (and Dimension X's successor program, X Minus One). The best of these include Bradbury's time travel story "To the Future" from May 27, 1950.
One of the single best Bradbury broadcasts is the Dimension X from June 17, 1950, featuring "There Will Come Soft Rains" and "Zero Hour," two quite different tales representing some of his best writing.
Dimension X did a great spooky version of "Mars is Heaven" from the Martian Chronicles on July 7, 1950, inventing some additional backstory for one of the characters which I think really enhances the tale.
The August 18, 1950 "Martian Chronicles" episode doesn't cover the entire novel - how could it, in just 30 minutes? - but it does get across most of the book's narrative, emphasizing mostly the bridging material which was original to the novel version of the story.
Yet another Martian Chronicles broadcast was "And the Moon be Still as Bright" from September 29, 1950, one of the very best tales from the story.
Bradbury's "the Veldt" covers familiar ground, especially when compared to "Zero Hour," but it probably makes a better case for itself than the latter story. Dimension X adapted "the Veldt" on August 9, 1951.
Finally, I don't think Bradbury's "Marionettes, Inc." is one of his best stories, but it's an effective thriller; Alfred Hitchcock Presents made a superior television adaptation of this story, but the radio version from August 30, 1951 is still pretty good.
Listen and enjoy!