If you do your research and find a reputable tattoo artist, tattooing is safe. A clean shop, clean equipment and new needles are a must. Talk to people around your area, get online and research the shop, it should be fine.
I asked my dermatologist about this and she cautioned that extensive tattooing can make it very difficult to detect an emerging skin cancer. If you are at a high risk for skin cancer, be thoughtful about the size and location.
In general, you are injecting a foreign substance under your skin. That just gives me the creeps right there. I don't even have my ears pierced!