The simple answer is that there is nothing wrong with tattoos.
Most people are content with that, but it helps to know why there's so much debate over them if there's nothing wrong with them.
The reason that many people say that tattoos are "wrong" or "sinful" is because:
A) They don't like them to begin with.
AND/OR
B) There is a Bible reference stating that the Hebrews were not to tattoo themselves.
First of all, tattoos are a matter of personal preference. Some people like them, and others do not. I know many Christians with tattoos, and many without. They all have varying opinions concerning the aesthetic value of tattoos, but they generally leave one another alone about them.
The one time tattoos are mentioned specifically in Scripture is in the Mosaic Law, under Leviticus 19:28.
NIV
Do not cut your bodies for the dead or put tattoo marks on yourselves. I am the LORD.
KJV
Ye shall not make any cuttings in your flesh for the dead, nor print any marks upon you: I am the LORD.
NKJV
You shall not make any cuttings in your flesh for the dead, nor tattoo any marks on you: I am the LORD.
MSG
Don't gash your bodies on behalf of the dead. Don't tattoo yourselves. I am God.
Now, in English, this seems pretty cut and dry. However, let's take a look at the original Hebrew to fully understand how they would have read into it:
The Hebrew word for the English term "tattoos" is "קעקע" (kah·ak·ah'). The understanding is a "stigma," from which we get the word "stigmata."
Before the invention of the tattoo needle in 1876 by Thomas Edison, and its modification by Samuel O'Reily in 1891, tattoos were imprinted under the skin by actually causing a wound in the shape of a specific pattern, rubbing irritants into the skin, and allowing the skin to scar over. It was much more similar to the modern practice of bloodletting or scarification than tattooing as it is known today.
The tattoo has often been associated with rebellious crowds, hence many Christians' hesitancy to accept them. They were discovered by Europeans in around 1766, with the crew of Captain James Cook. They ventured to the South Pacific, where the locals had been tattooing (in the scarification form) for centuries in accordance with their religious rituals. Several of Cook's crew came back from their voyages with tattoos, and the crew even brought back a chief who was heavily tattooed.
Yes, tattoos have pagan origins. That is one reason the Lord told the Hebrews they couldn't have them. However, once the Old Covenant was broken and we were put under a covenant of grace, tattoos were never given as a point of sin by Jesus Christ. In fact, God Himself told us that He looked at the heart of a man, not his outward appearance.
That said, it must be considered that while tattoos are permissible, they are not necessarily beneficial. I personally have no problems with tattoos and intend to get a few myself. However, through prayer and study, I have concluded the following concerning tattoos:
The first thing you should ask yourself is why you want to get a tattoo. If it's for your own self-glory, then forget it. Pride never bodes well. If it's to glorify the Lord, then by all means, go for it, but not without some other considerations.
Consider what you want on your skin. Remember, it's going to be there forever, even if you have it removed (the scar will be in the shape of your tattoo). Tattoos are not to be taken lightly. I know Christians who have naked ladies tattooed on their bodies. How much of a witness can you be with that? They say that women are beautiful creations of God and should be celebrated, but it's a sorry excuse to tattoo pornography on your arm. Pray about what the design should be. I can honestly say that God has helped me to design my tattoos that I will get.
Consider the cost, also. Cheap work isn't good, and good work isn't cheap. Your tattoo will cost at least $50 if it's decent, and that's not including the $10 tip you give your artist. Do your homework, pick a good artist, one that you're completely satisfied with, have him draw up the design, and then ask him: how much? Be prepared for triple digits. Always remember that God should be at the center of your stewardship, so it may not be a wise decision to spend your money on a tattoo.
Think about the area you want to get tattooed at. Again, this can be a part of your witness. That cross may look really cool, but can be really distracting when it's tattooed over your bladder. I saw a girl who had "God Rocks" tattooed right above her right butt cheek (she was in a swimsuit, and I was looking because I thought she had a sea urchin clinging to her hip). God may Rock, but don't plaster it in a distracting area. That's an issue between you and God where you want to put it.
Also do your homework concerning the parlor that you'll be tattooed at. Ask to see their health reports. If they won't give them to you, run away. Check with the Better Business Bureau to see if the parlor is registered (few are). Watch to see if the artist smokes, drinks, eats, or chews (tobacco or gum) as he works, or if he does any of the above near where he tattoos (even if he isn't working on someone at that moment). Do they wear gloves? Do they change their gloves between customers? Do they clean their equipment, or trash the old stuff and change it for every customer? Does the parlor smell like rubbing alcohol or drinking alcohol (the former being good, the latter being another red flag)? What kind of business will you be supporting? I once walked out of a parlor because one of the artists, although talented, had a bumper sticker on his portfolio that said "I Love Satan." He's an extremely good artist, but one that I will not support with my (read: the Lord's) money. There is a parlor just a few hours from where I live that refuses to do certain tattoos. They turn away probably $30,000 in business each year because they refuse to do demons, naked people, Satanic images, etc. They will only do family-friendly and/or Christian tattoos.
There are more considerations, but check out websites like xtat.org (The Christian Tattoo Association) for more information. Good luck!
Rob