Exposure to all sources of radiation -- including the sun, minerals in the soil, appliances in your home, and dental X-rays -- can damage the body's tissues and cells and can lead to the development of cancer in some instances. Fortunately, the dose of radiation you are exposed to during the taking of X-rays is extremely small.
Advances in dentistry over the years have lead to the low radiation levels emitted by today's X-rays. Some of the improvements are new digital X-ray machines that limit the radiation beam to the small area being X-rayed, higher speed X-ray films that require shorter exposure time compared with older film speeds to get the same results, and the use of film holders that keep the film in place in the mouth (which prevents the film from slipping and the need for repeat X-rays and additional radiation exposure). Also, the use of lead-lined, full-body aprons protects the body from stray radiation (though this is almost nonexistent with the modern dental X-ray machines.) In addition, federal law requires that X-ray machines be checked for accuracy and safety every two years, with some states requiring more frequent checks.
Even with these advancements in safety, it should be kept in mind, however, that the effects of radiation are added together over a lifetime. So every little bit of radiation you receive from all sources counts.