Six years ago my brother was considering applying to join the police force. Their rules, as I remember, were that visible tattoos were ok as long as they didn't contain hate speech, or anything religious/racist etc. I don't know if that's still the case, but that sort of ruling makes the most sense to me in jobs in the public eye.
I work an office job where I rarely, if ever, come into contact with members of the public/suppliers/clients. I have one visible tattoo, regularly dye my hair all the colours of the rainbow, wear loom bands (despite being 'too old' for them) and on Fridays, when casual wear is allowed, I'll come in wearing jeans and a geeky t-shirt. None of this affects the quality of my work, and as far as I can tell it doesn't affect the way I work with my colleagues. If any of them don't like my style choices they have kept it very quiet.
If I worked in a different position - more outward facing, for example, I would expect the same to be true. I would expect anyone I worked with to treat me professionally (and I them) and would expect any client or customer to judge me on the basis of my performance, not my outward appearance.
Nanny0gg - I understand what you're saying about there being a generational divide, however I don't think that's a particularly fair or valid justification for having a preconceived negative opinion of someone based solely on the way they choose to represent themselves.
Sorry for the essay - it's a topic close to my heart; I spent a long time after getting my visible tattoo worrying what affect it would have on how people saw me, when I should have been enjoying my new piece of body art.
One last thing - to those of you who think visible tattoos have no place in a professional environment, what do you think of make up? Are there levels of make up that aren't acceptable? I'm not talking full goth, but what if someone came to work made up ready for a night out clubbing; massive falsh eyelashes, very bold lipstick etc, how would you feel about that? Is there some sort of conservative dresscode you would accept? Why?