Those not convinced by the safety of backscattering X-ray machines being rolled out throughout our airports can 
seek a peace of mind from Rocky Flats Gear, a company manufacturing undergarments for blocking radiation shining at private parts. The non-lead lined (not sure what the actual material used is) underwear and bras can also be helpful for paranoiacs getting dental X-rays and radiologists working the foot pedal on a fluoroscope.
From the company:
Rocky Flats Gear is the US manufacture of a revolutionary flexible, attractive, lightweight, Lead (Pb) free, radiation shielding garments for individuals. Our emphasis is on protecting the traveling public, airline, medical, and security professionals from radiation generated by security and medical imaging equipment. Our novel products can protect tissues from a broadband of ionizing and non-ionizing radiation generated by imaging equipment and natural sources. For the first time, radiological shields are attractive, durable, affordable, fun, and comfortable to wear.
Link: Rocky Flats Gear …
(hat tip: /.)