There are verses in the Old Testament that include laws for the Israelites to follow in order to show that they were separate from the rest of the world. Verses like Leviticus 19:28, "Do not cut your bodies for the dead or put tattoo marks on yourselves. I am the LORD."
At that time in history, some religious cults would perform various practices (see Leviticus 19:26-27), including making marks on their skin to honor the dead or show faithfulness to their gods. Obviously, God did not want the Israelites to ever be mistaken for those groups because of something they did. That's totally legit.
“Each week we sit under the word of God together, opening our selves not primarily to information, but to transformation.”
First Corinthians 10:31 says, "So whether you eat or drink or whatever you do, do it all for the glory of God." Will your tattoo or body piercing glorify God or go against Him? What is your motivation for wanting to get one done (2 Corinthians 13:5)? Is your heart in a place of godly peace or rebellion (Proverbs 30:17)? Is the question of whether or not to do it causing bad things to happen in your life (1 Thessalonians 5:22)?
If getting a tattoo or piercing or dying your hair is going to cause problems or hinder your ability to be more like Christ, then you should seriously re-consider that decision. This is a matter between you and God. Ask Him if it would be a good choice for you and how He can use it in your life.
There is a lesson in Romans 14 about how we should not do anything that would cause another believer to stumble. The story goes that Christian Group A did not want to eat meat that was sacrificed to idols, but Christian Group B thought, "What's the big deal? I don't believe in that god, and I am not letting a good steak go to waste." The author says that Christian Group B should not eat that sacrificed meat in front of Christian Group A because, to them, that meat was sinful to eat.