Is it a sin to get a tattoo?
The Jews were forbidden to perform certain acts for the dead that were common among the heathen nations around them. "Ye shall not make any cuttings in your flesh for the dead, nor print any marks upon you: I am the LORD." (Leviticus 19:28) "Ye are the children of the LORD your God: ye shall not cut yourselves, nor make any baldness between your eyes for the dead." (Deuteronomy 14:1) These laws were specifically for the Jews, and do not necessarily apply to Gentile Christians. The principle is that even in times of mourning we are not to do anything that would make it appear that we are questioning God or giving up our faith in God.
The other mentions of marks on bodies don't really apply to whether we can have tattoos or not. Cain was given a mark so that others wouldn't kill him (Genesis 4:15), but whether that was equivalent to a tattoo or not we don't know. Ezekiel tells of a figurative "mark" given to the faithful (Ezekiel 9:4-6) to save them from the wrath of God. The book of the Revelation to John, chapters 13-20, mentions the "mark of the beast" that was put on men (probably also figurative), to show that they followed the Roman government (the beast of Revelation). As I said, whether these marks could be considered tattoos is questionable. If they are, Cain's doesn't apply to us, and the others are figurative and not literal.