I know some here feel it is wrong, that we are to keep our bodies as natural as possible as they are temples of the Holy Spirit once we are received by Christ. I have a tattoo myself, because it was done years ago.... I can't say I regret it, but if given the chance, I probably would not have it done again!
I don't personally think there is anything immoral about having a tattoo... I know they are not a natural part of our body, but neither is a woman who wears lipstick and mascara every day -it's all addition to the natural body in one way or another. As is wearing jewlerry, or dyeing your hair a different colour. The difference is, of course, that tattoos are permenant, so be careful that you really feel sure about having one.
I saw some beautiful Christian tattoos recently, of Christ and the fish symbol. Some love it, some hate it. Some think it's wrong. One thing I will say, is that the Christian tattoo causes people to ask questions, it's like an opening to evangalise because the tattoo gets peoples attention - perhaps in that way it is a good thing. "So, how long have you been a Christian?" or "What does that fish symbol mean?" etc. Do you get my drift? Good can perhaps come of something like that.... but it's a mixed bag. We are to treat our bodies so well, as followers of the Lord...the more I think of it all, the more confused I feel about this subject....!!