I think tattoos look unprofessional. There, I said it.

I'm not anti-tattoo, I just think that people should have the foresight to put their tats where they can be covered when appropriate. In their personal lives, expose away.
I work in a fairly conservative law enforcement setting. Everyone looks clean cut until shirts are removed in the gym and you see guys with 20 tattoos up above the short sleeve lines and all over backs and chests. If they had exposed tattoos during their interviews they wouldn't have been hired. Maybe it's fair, maybe it isn't, but it's the way of the profession. You have to look the part.
I think the current trend towards loads of tattoos will die out because they are no longer unusual and (when I was younger at least) the people who chose to get them were the more anti-establishment type. It's no longer rebellious.
As far as tats on teachers, I don't care but I think I'd have to wonder about someone with a scroll crawling up his neck or something.
It would be ok I guess for a high school teacher but I wouldn't want my kindergartner influenced by neck art.