Thanks everyone for all the responses. I personally don't mind them on a female as long as they aren't tasteless.
The worst tats that I have ever seen were scleral tatoos. I asked a young man if his eyes felt OK; he had bright red eyes (where they are supposed to be white) and he replied, "Oh, they are tatoos." The white part of his eyes had been tatooed bright red.
I have seen foreign body reactions and benign masses below tatoos, so they aren't completely harmless.
I like to know why they have it, and the story of it, but even beautiful tattoos can seem ugly in the wrong place. So I guess my go to rule is, "can you cover it up if you don't want to see it?" This basically gives the person an escape if they don't want to have it in all their wedding/graduation/special event photos. It's the same with piercings.
And like all things, all in moderation. :)