If you have hemophilia. There is even a case of a man who was HIV positive who got a tattoo--if you are HIV+ however, you will want to inform the artist, since it's the artist that is at more risk than you. [In the case of the HIV+ man, he was John Baldetta, a former nursing assistant at Harborview Medical Center in Seattle, who got a tat on his forearm that said "HIV Positive." He was suspended for three days without pay and told he could return if he covered up the tat. He refused and was subsequently fired, although he was not an RN and was not doing anything that would put patients at risk. However, it is best to let the artist know if you have ANY medical condition, such as diabetes or epilepsy, in case of an emergency.
If you have multiple allergies, you can always have the artist do a "patch test" on you with the colors you want prior to returning for a regular tattoo. This is similar to patch tests done for perms and hair coloring, and will help you determine if your body will react to some of the pigments.
Also, it is generally not considered a good idea to tattoo pregnant women.