NET (New English Translation) – You must not slash your body for a dead person or incise a tattoo on yourself. I am the LORD.
JPS (Jewish Publication Society) – Ye shall not make any cuttings in your flesh for the dead, nor imprint any marks upon you: I am the LORD.
ESV – You shall not make any cuts on your body for the dead or tattoo 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 (ASV is similar).
Every now and again I am asked about what the Bible says about tattoos, especially what does the New Testament say. The New Testament gives no attention to the topic, but as you can see, the words of the Lord in the Old Covenant are rather plain. As you look at the above verse, notice the Lord makes a distinction between cutting (slashing) one’s body for the dead and a tattoo, or marks of any other nature.
It has been said that tattoos have been around since who knows how long! Be that as it may, in the last 50 years it has taken a far-worse turn in direction. Some people have more ink on them than they have the color of their natural skin exposed. Evidently, they think it looks good.
At one time, the Lord did not. When did He change His mind? “That’s the Old Testament!” one might say. True enough, but so is Leviticus 19:29.
Can one be pleasing to the Lord with all the mark-ups on their body? Of course. The key to salvation is the heart’s response to His will and obedience to follow thereafter. The markings on the body, whatever may be said of them, does not have to be a true representation of who that person is.
etsop95 
I do not think Lev 19:28 and 19:29 are fair comparisons. As you said, tattoos are not mentioned in the NT. But prostitution is mentioned in the NT.
For a better comparison, is there another practice that the OT condemned and that the NT does not mention?
19:32 It is a good comparison because it is the same text. Where is the teaching or spirit of 19:29 in the NT, apart from the general classification os sexual immorality?
Cool. I agree, 19:32 is a better comparison with verse 28. For Christians, the prohibition of tattoos would be in the same category as the teaching that people must stand up for the elderly.
Lev 19:29 prohibits employing someone (example of a daughter) into prostitution. 1Cor 6:15-16 prohibits someone from employing a person into prostitution. The teachings are very, very similar. The spirit behind how God feels about prostitution is the same.