Now, I suppose one could make the case that The Bible says our body is a temple to The Holy Spirit and that by marking it up, we're defiling that temple. But, I'm not really sure if that would count as defiling the temple of The Holy Spirit. That brings up the question: What counts as defiling The Holy Spirit? I suppose if one gets tattoos depicting sinful things (e.g half naked ladies, genitals, curse words, satanic symbols, etc.), that could and would offend The Holy Spirit. But some people, like Brian "Head" Welch, the Christian Rock artist and former member of Korn actually gets Tattoos in order to bring attention to Christ. Ironically, before he became a Christian, he didn't have that many tattoos at all. He said in his autobiography that he actually got a ton of faith based tattoos after he became a Christian and he said it was to bring attention to and glorify God.
So....I don't know. I don't really take a position on that per se. I kind of think it's ok as long as it glorifies God, and doesn't depict anything sinful. But I also know that some people feel very strongly against the idea and they probably have reasons for being against them (although as I said before, the Leviticus argument fails, so that's not a good reason). I WILL SAY that if you feel convicted, you definitely should not get a tattoo. If you feel that The Holy Spirit is telling you not to do it, don't do it. Also, for pro-tattoo people, don't try to persuade someone who DOES think it's sinful to get a tattoo to get a tattoo. 1 Corinthians 8:12 says that "when you sin against other believers by encouraging them to do something they believe is wrong, you are sinning against Christ". It doesn't matter if it's ACTUALLY wrong or not, the point is not to put pressure on another believer to do something that violates their conscience.
I would also advise those against tattoos to not make a big fuss about it if you see a person professing to be a Christian inked up. There are far bigger issues we have to deal with in the church wouldn't you think? No need to be so judgmental. Jesus said that it's what comes out of a person’s heart from the inside that makes a person unclean (Matthew 15:18). We don't know the hearts of men. Only God does. Someone with tattoos covered from head to toe may be more Godly than someone who doesn't have the slightest jot or title on them.