If you want to amuse yourself, type the question 'Should a Christian have a tattoo?' into an internet search engine and watch the sparks fly! Some people see tattoos as okay while others see them as 'evil' and inappropriate for a Christian.
The Bible teaches that God is holy and that he has called us as his people to be holy also. 'Holy' means set apart to the Lord. Holiness is primarily a matter of the heart and it refers to what's happening on the inside of us. This was the focus of Jesus' teaching (see Matt.5-7 as an example).
There are many misconceptions about what holiness is, including an overly strong emphasis on external appearance and particular stances on a variety of non-sinful issues. Having a tattoo does not necessarily make a person 'unholy' nor does not having a tattoo make a person 'holy'.
I don't think you can build a water tight Biblical case against tattoos. It is only mentioned once in the Bible ...
Lev.19:28. "Do not cut your bodies for the dead or put tattoo marks on yourselves. I am the Lord." NIV
If you take this as authoritative and with direct relevance to today then you shouldn't cut your hair on the sides or trim the edges of your beard, as instructed in the previous verse.
Lev.19:27. "Do not cut the hair at the sides of the head or clip off the edges of your beard." NIV
You also shouldn't wear clothing with mixed materials, as mentioned a little earlier in this same chapter.
Lev.19:19. "Do not wear clothing woven of two kinds of material." NIV
Are you weating a cotton and polyester piece of clothing today?
These prohibitions were primarily aimed at ensuring that Israel avoided pagan religious rites. God was clearly forbidding them from various forms of occultic and pagan worship (see also Lev.21:5). Lacerations and disfigurement of the body were common among pagans as signs of mourning and to secure the attention of their deity (see 1 Kings 18:28). These laws were specifically forbidding pagan mourning practices involved in ancestor worship, both of which were major components of life outside of Israel (c.f. Deut.14:1-2. Jer.48:37).
Today there is no earthly ritual system with reference to which we can make distinctions in this way, so the applicability of these laws has ceased to exist. They are no longer directly relevant to us today.
So that leaves the matter of choosing whether to have a tattoo or not as a conscience issue for each individual.
So what principles would we apply to whether or not a Christian should get a tattoo today?
The following questions are worth at least considering:
Why do you want a tattoo? Is this just to follow a trend?
What do you want a tattoo of? There is a big difference between a cross and a snake (or a nude body)!
Have you really thought through the ramifications? Tattoos are permanent and don't come off. For instance, tattooing "I love Mary" on your arm may not go down too well if you end up marrying someone named Jane! I heard a story recently of a woman asking for a tattoo of the name "Brett", only to discover the tattooist made a mistake and tattooed the name "Bert" instead! Of course that's better that a recent article in our local paper of someone going to Thailand and asking for a tattoo of the words 'Geelong Cats - Day Premiers' to be placed on their right arm, only to discover that that tattooist got it wrong and wrote 'Geelong Cats - Gay Premiers' under the actual words 'right arm'!
How big is this tattoo you want? There is a big difference between a small tattoo and covering your whole arm, leg or neck, for instance.
Where is this tattoo going to be? There is a big difference between something discreet than one on your face, for instance.
As far as parents and teenagers, this is an issue for the parents to sort out, not for the church to make a ruling on. Our church does not have an official stance on this issue. Parents have the God-given authority to make a decision either way on this issue for their teenagers (as they do in other areas such as whether to allow them to see certain movies, etc). Teenagers need to obey and honour their parents on matters such as this. Obviously, teenagers may ask 'why' and parents need to be prepared to answer this (which may simply be - "Because I said so", although a more in-depth discussion may be more beneficial).
This is no doubt a controversial issue but we must separate 'Biblical mandates' from 'personal convictions'. Both are necessary and important but we must not confuse the two.
P.S. As far as people who already have a tattoo ... church communities should seek to be places that accept people as they are, not based on certain criteria on debatable issues. We want people to feel loved, welcomed and valued - just as they are, in the same way that Jesus did.