This Old House does a good job of summarizing the controversy behind the granite-countertops-emit-radon argument. This radioactive gas can cause lung cancer, so any radon is a very real danger, however, the EPA issued a statement saying there isn't enough evidence to suggest granite countertops are a source of radon. And if you're still worried, pick up a home testing kit for $25. If you'd like to ditch your granite altogether, check out the myriad of countertop options you have here.
Best keep looking for info on this topic rather than believe the stone industry. Way too much money at risk, plus the have sucessfully covered this up for the past 14 years. They canít tell the truth, so they keep digging the hole deeper.
If this was a non issue, neither the CRCPD (state radiation officials) nor AARST (radon scientists) would have committees seting maximum allowable radiation/radon levels for stones and measurement protocols. ANSI and ASME are also looking into the controversy for their organizations.
On the radon issue, we have a full scale radon test going currently, over 10 pCi/L so far from only 18square feet of granite in a 96 square foot room. That is like smoking 1 1/2 packs a day, http://forum.solidsurfacealliance.org/viewtopic.php?f=7&t=98ST
We have a lot of info on the topics available.