If you want to find where in the bible it says its wrong to abuse your body, you can find it in Corinthians 3:16,17.
16.Do you not know that you are God's temple, and that God's spirit dwells in you!
17. If anyone destroys God's temple. God will destroy that person, for God's temple is holy, and you are that temple.
Not only tattoos, but drugs, alcohol, cigarettes, and any kind of foreign things that the body does not need to live on is included.
My question is 'Why do people want tattoos?' My thoughts on this is that the only reason anyone want a tattoo(s) is to attract attention. Why do they want attention? It's because they are insecure about themselves. The same goes for those who dress a certain way, dye thier hair a bright color, or drive a certain type a car. Status is important to them and often they want to be like everybody else.
I do believe its one's choice to do what they want to themselves, but I prefer to keep what God has given me. What God has given me is a gift, and one needs to take care of, and appreciate God's gift by not using and abusing it.