Dental X-rays are not 100% free of risk. However, they are very, very low risk. Given people take risks with radiation every day (going into the sun, eating bananas), it is reasonable to accept the risks of dental X-rays to gain the health benefits associated with their diagnostic abilities.
This xkcd info-graphic puts the risk in perspective - click to expand and then see dental Xrays at 5 µSv in the top corner):
But what are the actual risks from these doses?
(Note: Some of these studies are dated - I would expect that modern technology, the amount of radiation required has been reduced and the ability to treat the malignancies has improved, making these over-estimates of the current risk levels.)
Our results indicate that in the UK about 0·6% of the cumulative risk of cancer to age 75 years could be attributable to diagnostic X-rays. This percentage is equivalent to about 700 cases of cancer per year.
A 1983 study in the UK suggested that, depending on the type of dental X-ray, the risk of fatal malignancy from dental x-rays is up to 1.3 per million, suggesting that accounted for no more than a total of three extra fatalities per year.
A 2004 study found the risk of getting an intercranial meningioma roughly doubled - remember this is from a relatively low base-rate).