There is ongoing research as to the amounts of exposure and the risks, but the scientific community's current position is that the risks are typically low and justified by the benefits.
The actual amount of radiation depends on the type of test. The average person is exposed to 2.4 mSv yearly from medical testing, a low amount. However, a small group of Americans (comprised mostly of seniors and females) receive a cumulative annual exposure of 50 mSv or more from medical scans. That is 2 1/2 times the maximum amount permitted for workers at a Nuclear power plant.
Recent studies suggest that 2%-12% of cancers in the U.S. may be due to over-exposure. So, hopefully, doctors have learned, as with the over-prescribing of anti-biotics, that unnecessary medicine can have harmful results.