As cutiesmak suggested, there is a prohibition of Tattoos in the OT law. Leviticus 19:28, in the NAB this reads as follows: “Do not lacerate your bodies for the dead, and do not tattoo yourselves. I am the LORD.” While this is not necessarily applicable to us, this is enough to give me pause.
One might wish to consider that a Tattoo could be a scandal to those who do believe ill of them, even if you disagree. In the U.S. at least they are sometimes perceived as emblems of rebellion against parental or other authority.
I have been told that tattoos were condemned at the second council of Nicaea, but I have not verified this claim from an authoritative source.
There are also some health risks associated with tattoos, but those risks are far less than for piercing.
Personally, I don’t find them appealing anyway.