Mammograms are absolutely necessary. It is an easy, cheap, and effective way to provide early screening. Sure, it might not catch everything, and there might be cases of worry over nothing, but it is still better to go through the process just in case. It is a great preventative tool that can help save lives without much effort.
The purpose of the mammogram is to examine the tissue within the breast, typically to check for cancerous markings or to examine any abnormalities. This IS important. With all of the carcinogens in every facet of modern life, tumors can develop and be undetected by normal means until it is too late. While this may seem unlikely to some (after all, women can do self-examinations, right?) it is important to remember that the breast is made up of glands and fat. Both of these things tend to shift and sometimes gather together and can be mistaken for 'lumps'. Or actual lumps can be overlooked as 'normal'.