Angela and I, (my real estate guru, as well as my wife) have been talking about Radon in homes as of late.  In the last twelve months, she has had some existing homes she listed, test positive for radon slightly above safe levels.  These homes are located in areas where radon was previously unknown.  She has had to have discussions with sellers and buyers regarding having radon mitigation systems installed.  These systems can be retrofit, but is easiest to install when building your new home. 
If you are concerned about radon in your own home, you can test for it.  Check  your local directory for listings for radon testing.  If no listings, check with your local real estate office.  They will have some contacts for this testing.
If you have a positive test that is above safe levels, then you have two systems available: passive or active systems.
Passive systems can control up to moderate amounts of radon, and have no moving parts to maintain.  Passive systems utilize a pipe which goes from below the basement floor, and continues vertically until it exists the roof of the home.  Air movement across the top of the pipe creates a chimney like effect, drawing air, from below the floor to the exterior world.  It gives an exit path for radon to leave the building, without entering the living areas.
An active system uses a pipe which is installed the same way, but uses a powered inline fan to created a vacuum under the basement floor.  This removes larger levels of radon from beneath the floor, before it can enter the living areas.  The picture below shows Angela learning about an active radon mitigation system at the international Builders Show last year.