Radiation is always a concern with X-Ray examination - however, if a physician requests an X-Ray examination it should be because it will assist in making a medical decision. The benefit from the X-Ray should outweight the small risk of the examination - this decision is made at several levels - the physician requesting the examination, the radiographer who is to operate the X-ray equipment, and the radiologist, a physican with special training an experience in X-ray examination.
The radiation exposure from different types of X-ray examination varies widely. An X-Ray of the abdomen uses about 50x as much radiation as a chest X-ray (1 mSv). A CAT scan of the head is about 100 chest X-Rays (2 mSv), and a CT scan of the abdomen + pelvis is about 1000 CXRs (20 mSv). (As a point of reference, a one-way transatlantic flight is an equivalent radiation exposure to a CXR). A chest X-Ray exposure is typically 0.02 mSv. Background natural radiation is about 2-10 mSv per year depending on the area.
The data regarding health effects of very low radiation exposure is rather limited, but the best available data suggest that a CXR carries about a 1 in 1,000,000 risk of causing a cancer within the following 50 years, and a CAT scan of the abdomen about 1 in 2,500. (4% per Sv).
These are low risks, and high-radiation examinations are not carried out without good reason. If I was ill enough to need a CAT scan , then the effects of radiation would be the least of my problems. The short answer is that if you need multiple X-rays, the chances are that you are ill enough for the potential risk of the radiation to be less than the risk of the illness.
The potential risks of X-ray radiation are the reason why much effort is being focused in the direction of imaging techniques such as ultrasound and MRI (Magnetic resonance imaging). However, in the emergency room, simple old-fashioned X-rays of bones, chests and abdomens are likely to be with us for a long time to come - the are readily available, quick, and will give you the most important diagnoses.
Nevertheless, even though these newer techniques do not use X-rays or ionizing radiation, there may still be risks. MRI doesn't use ionizing radiation but there are definite risks - the most significant is the risk of the extremely strong magnetic field on metal objects - metalic implants such as artery clips (used in brain surgery), or pieces of shrapnel in the eye (from industrial injuries - sometimes, not even noticed at the time of initial injury) can move in the field and cause serious injury. Of course, the objects don't have to be inside to cause damage - there are recorded instances of people being injured by other objects - for example a patient was brought into the scanner room on a normal (steel) wheelchair, instead of a MRI compatible (aluminium) one. They ended-up pinned to the scanner by the wheelchair, which in the end needed 8 people to remove.
I'll admit that I have had a couple of MRI scans just for fun, and I don't think that I put myself at undue risk because of it. However, time will tell; after all, for over 50 years, X-rays were considered totally safe, and even beneficial.