I have a tattoo I got this last summer on my back. My husband, I, and many MANY Christians in southern California have tattoos. In fact, our tattoos were done by a Christian-centric tattoo parlor whose owners and workers attend Calvary Chapel.
My own tattoo was designed by myself and is deeply spiritually meaningful (both the design and the marking of my body), and was done after about a decade of thought and prayer about it. Tattooing means different things to different people- some just like the look of it, for some it is following a trend, for some it is a deeply moving experience that coincides with important events, beliefs, etc.- marking the outer "you" with expressions of the inner "you."
I'm actually thinking of making it my avatar at some point. It starts at the base of my neck and goes between my shoulder blades. It is a Celtic cross in a Celtic knot-work design, with a triple spiral in the center of the cross. The symbols summarize many of my beliefs and spiritual experiences. I wanted to permanently mark who I am, spiritually, on my body. I suspect this would not make sense to some people, but then we are all different.
As for the Biblical basis for not tattooing, as far as understand it...
1. I am not Jewish, so I am not bound to the mitzvot. I am bound to the Noahide laws, which I follow. I am allowed to honor the ways of my own ancestors, of which tattooing was a part, so long as I worship the One God.
2. The Biblical commands against vanity or adornment do not apply to tattooing if it is not done with such intent. My tattoo is almost always covered up. I did it for me, and in honor and worship of God, not for other people. Further, this type of argument is rather hollow unless the person making it extends it to all its original meanings, including no wearing of jewelry, expensive or elaborate clothing, etc. The vanity arguments are not about tattooing, but about monetary cost and adornment. In which case, they are much better applied to our culture as a whole, which encourages people to spend lots of money on name-brand clothing, diamonds, and so forth. In this line of reasoning, we should all be dressing "plain"- like Mennonites or Amish.
Bottom line, I don't feel my tattoo (or anyone else's) is a sin. It didn't harm my body. It healed faster than a light sunburn, didn't hurt much, and isn't harmful like suntanning. If it's all about the "body as temple" argument... well, God gifted me with a brain that is artistic and creative and a body to decorate with spiritual artwork. I don't see many churches or temples (outside of the "plain" religions) that are undecorated.
It is in our motivation, not the action itself, that sin may lie. If our motivation is vanity, we are being sinful because of that motivation. But the action can be motivated by many different things.
My left arm sleeve... Ever seen the Hellraiser films? Where there is a "sculpture" of human bodies entangled and in distress... That is my sleeve 
