It's your own body. If you want to cover it in ink, have so many piercings you can't get through a metal detector, stretch your earlobes until they hang to your shoulders, or have your teeth filed into points, then that is, and should be, your right. As long as a person is over the age of 18, and fully realizes the consequences of what they are doing, then they should have the right to do it.
Yes, I believe that people should have the right to do what they want with their own bodies. The only person that owns you physically is you. As long as it is not physically hurting someone else in the process, then a person should have free reign over the things that he or she does or allow another to do to their body.
I think that people should have the right to do whatever they want in regards to their own bodies. While some of us may not agree with some of the weird tattoos and piercings some people get and do to their bodies, as long as something is not illegal, it should not be prohibited.
I don't believe people should have the right to do what they want with their own bodies because that would leave it open for people who are extreme expressionist. They could harm themselves (mutilation, branding, etc) severely where they might need medical treatment which would lead to unnecessary resources being used, medical, police, etc.
I don't believe people should have the right to do what they want with their own bodies. This is because it can lead to too many suicides or drug and alcohol-related deaths. Just because a person can do something to themselves, it doesn't mean they should. We need to care for our fellow human beings and not encourage their demise.