I'd wait til after the baby is born. I've been to many tattoo places (going with friends who were getting some done and a couple times myself), most artists will not tattoo a pregnant woman. It's a whole liability thing, same with if they tattoo someone who is anemic. If the woman loses her baby after the tattoo, they can be held responsible causing a major lawsuit.
Tattoo's cause stress to you, worrying about the pain, if it's going to look good, then the pain of the needles stabbing you over and over. So with the stress caused to you, multiply that by say 1000, that's how much stress it causes to your child.
I'm not going to get into the diseases that you can get from a place.. Everyone else seemed to cover that.
But remember, when you do go to get a tattoo.. Make sure it is something that you wouldn't mind having on your body the rest of your life. I got in a tattoo mood one day, and got a playboy bunny on my lower back. Now i'm saving up to get it covered up lol.