X-ray for back pain–the pain usually stems from muscle damage and clears up on its own within a month or so.
Chest x-rays before surgery–According to the American College of Radiology, you generally need the test only if you have lung or heart disease, you have signs or symptoms of a heart or lung condition or you are scheduled for surgery that will involve the heart, lungs, or part of the chest.
CT scans to screen for lung cancer–The American College of Chest Physicians, among other groups, says that the test is worthwhile only for people at the highest risk of developing lung cancer, current or former smokers between the ages of 55 and 80 who smoked the equivalent of a pack a day for 30 years.
CT scans for headaches–The American Headache Society says that’s necessary only if your doctor can’t diagnose your problem based on a physical exam, which he or she almost always can.. Some red flags include headaches that are sudden or explosive, or those accompanied by fever, seizure, or vomiting. But in those cases, MRIs which don’t expose you to radiation, are often a better choice than CT scans.
Source: Consumer Reports on Health March 2015