I am often asked whether it is possible to download old radio shows that Bradbury was involved with, or shows that adapted his stories. The answer is yes, but don't expect to be able to find everything. Some material (very little, admittedly) is available commercially on tape or disc; visit my audio page for some links for specific shows, but don't be surprised if the shows are no longer available.
One of the better download sites for old radio shows is Zootradio. You have to register (for free) for access to the downloads, but it holds a wealth of material that in my view beats any other free site on the web. For Bradbury material, you should head straight for Dimension X and X Minus One. These series presented a number of Martian Chronicles stories, and other gems such as "Marionettes, Inc".
Unfortunately, another site that was good for the occasional Bradbury gem, Gwangi's Blog, looks like it's closing soon, at least as far as live download links are concerned.