The New York Times debunks the myth
that "If you get a tattoo, you can’t be buried in a Jewish cemetery":
The eight rabbinical scholars interviewed for this article, from institutions like the Jewish Theological Seminary and Yeshiva University, said it’s an urban legend, most likely started because a specific cemetery had a policy against tattoos. Jewish parents and grandparents picked up on it and over time, their distaste for tattoos was presented as scriptural doctrine.
But even if the cemetery thing is a myth, some scholars believe that tattooing itself is against Jewish law:
Rabbi Alan Bright, a spokesman for the Jewish Funeral Directors of America, dismissed the cemetery adage as “a load of rubbish,” but he said that tattooing was a no-no. He quotes Deuteronomy 4:15, which commands Jews to take care of their bodies, as evidence. But he noted that Jewish law prohibits many things that secular Jews do without a second thought. “The Torah prohibits anything negative that affects the body,” he said. “Smoking is more of a violation of Jewish law.” As are drinking alcohol in excess and overeating.
Not being Jewish, Jewish law has played little role in the fact that I've never gotten a tattoo. Though I have considered getting a small jackalope tattooed on my ankle.