Various stories on radioactivity being found in granite countertops have popped up in various places over the past several weeks, most of them pushed very strongly by a specific advocacy group (a group that lobbies on behalf of synthetic countertop makers). There's not a lot beyond the scare tactics of the story, so I don't think there's any reason to pull out your granite; that said, some scientists have gone on the record as saying there are rare cases of significantly radioactive countertops, so it is something to think about.
“It’s not that all granite is dangerous,” said Stanley Liebert, the quality assurance director at CMT Laboratories in Clifton Park, N.Y., “But I’ve seen a few that might heat up your Cheerios a little.”
The E.P.A. recommends taking action if radon gas levels in the home exceeds 4 picocuries per liter of air (a measure of radioactive emission); about the same risk for cancer as smoking a half a pack of cigarettes per day; a few granite countertops exceed this, but not many. But others, like Lou Witt of the EPA, say “There is no known safe level of radon or radiation.” Moreover, he said, scientists agree that “any exposure increases your health risk.” New York Times
Of course, completely secondary to the radioactivity issue, Granite is not an environmentally sound choice for countertops: the mining is incredibly devastating, it's often shipped around the world for processing and cutting, and it is - obviously - completely non-renewable. The fact that it may outgas radioactive substances and contain radioactive ores is now something else to worry about, or maybe Mother Nature's revenge for being assaulted.
Thanks to Treehugger for digging a bit deeper (at least, deeper than the New York Times or anyone else had bothered to).