Dental x-rays are a necessity for diagnosing disorders in your mouth, such as tooth decay and gum disease. Without x-rays, a dentist will not be able to find early problems in your mouth as they are not apparent by any other means. A full mouth set of x-rays or panoramic x-ray will disclose tooth nerve problems, impacted teeth, bone tumors and jaw fractures.
A few examples of things not visually detectable include tooth decay between your back teeth, loss of bone around your teeth and impacted teeth. The risks you take to your oral health if you refuse x-rays are far greater than any there may be from having those x-rays taken.
Finding dental problems early on will prevent much larger difficulties for you, including less discomfort, less treatment and less expense.