Strict guidelines are in place to ensure that mammography equipment is safe and uses the lowest dose of radiation possible. The truth is that a woman is exposed to more "background" radiation in her daily life than when she receives her annual mammogram.
Unfortunately, there is a lot of bad information out there, especially on the Web. Be sure to look at the source of the information you are reading. If it is something you hear from a friend or colleague at work, be sure to double check what they've told you by searching the medical literature. If it is something you read online, make sure the website is reputable, and the information has been carefully reviewed by medical professionals affiliated with clinics, hospitals, or research institutions. Don't believe everything you hear or read, without further checking it.