Getting your twice-yearly cleaning and dental exam should be a quick task, but it seems like you're constantly being led over to the x-ray chair to get more pictures of your teeth taken. If you've got teeth that have always been in good condition, this can seem like overkill with the x-rays. Is it always necessary to get so many x-rays of your teeth? The answer depends on how new you are to the practice, how long it's been, and what else you're planning to have done -- as well as your budget.
You don't need x-rays at all of your dental exams, of course, unless you come in with a specific problem. Many people stick to getting x-rays every other cleaning, but if your teeth have been very healthy for a long time, and you've had no dental problems, you may want to discuss the x-ray schedule with your dentist. Keep in mind that your dentist will still need x-rays every so often because those are really the only way to tell if something is wrong with your teeth. Many people have cavities without having other symptoms like pain. And if you do have pain, that alone isn't good enough to tell if something is wrong; for all the dentist knows, maybe your tooth pain is just sensitivity and not a cavity.
What you want to aim for is an interval that allows the dentist to track your tooth health frequently enough to prevent small problems from becoming huge. You don't want to wait several years and then find that a minor cavity grew into a need for a root canal; you want to catch the cavity quickly and fill it. Generally waiting a year or so between x-rays is sufficient, but if you are still unhappy with that and want to extend it, talk to your dentist. This is a part of the exam you do need to get occasionally, but as a patient with rights, you can negotiate that frequency.
Do be aware that if you're a new patient at a practice, you'll really need to have x-rays done. The dentist needs a baseline to understand what's going on with your teeth. If you recently had x-rays done at your previous dentist's office, you might be able to have them sent over to the new office instead of getting another set taken.
Of course, cost can be a deciding factor as well. If you have no dental coverage and do not want to take on a lot of credit card debt or apply for a dental credit loan, then getting the cleaning is more important, if you have to choose procedures. In this case, you do have the right to ask to skip the x-rays; the dentist, of course, can always tell you to find another dentist in that case, though. After the Great Recession, however, more dentists have been willing to work out alternative scheduling for those who are dealing with tight financial resources. For example, maybe right now you'll get the cleaning and a visual exam, and then in a few months you can come back for x-rays.
Talk to your dentist about your concerns. Good dentists can work something out with you.