Makkos, Chapter 3, Mishnah 6. This mishnah deals with the prohibition of a tattoo. There are two components in this expression: "kosev" - writing, and "ka'aka" - engraving into the skin.
The conditions for liability according to the mishnah:
"kasav v'lo ki'akei'a" - he took the ink used for tattooing and wrote with it on the skin, but did not engrave or cut into the skin - he is not liable.
"ki'akei'a v'lo kasav" - he cut into the skin but did not use ink at all - he is not liable.
He is liable only for writing and engraving together, "bidyo uvakchol uv'chol davar shehu roshem" - kchol (blue dye) is one form of ink, and likewise any other substance that leaves a mark.
The view of Rabbi Shimon:
The mishnah brings an interesting qualification in the view of Rabbi Shimon: one is liable to lashes for making a tattoo only "ad sheyichtov es hashem" - until he writes the name. And which name is meant? The name of an idol. If he wrote the name of the idol, that is a violation, and if not, he is not liable. He derived this from the wording of the verse that forbids this writing, from which it is evident that a tattoo is an act of allegiance to idolatry. So says Rabbi Shimon ben Yochai in the name of Rabbi Shimon, and this is why, in his view, a tattoo is forbidden only when it is the name of an idol.
In practice we do not rule like Rabbi Shimon; rather, all forms of tattooing are forbidden by the Torah, and one who makes them is liable.
A person's ownership of his body:
Tattoos have become very widespread in the world around us, and to a certain extent they express the outlook that a person is the owner of his own body. This outlook stands in contrast to our own, that our body is not ours but belongs to Hashem, and that we must treat it with respect.
The myth about burial:
An idea that has spread among the Jewish people, especially among those who are not religious, is that a person who has a tattoo cannot be buried in a Jewish cemetery - and there is no source for this anywhere in the Torah. My guess is that Jewish mothers, who did not want their children getting tattoos, told them that they would not be able to be buried with the family. That is the only explanation I have for how this became such a widespread myth.