It depends where you would like to work.
For example, I worked for a mortgage company and we were allowed to wear whatever we wanted and have visible tattoos and/or piercings because the owners of the company believed that if we were comfortable in our environment, our performance would be better. In this case, it was absolutely true.
Currently, I work at a mortgage brokerage and I am not allowed to have visible tattoos. They let me keep my monroe in because they say it is "discreet" (it is just a tiny little gem).
All of my tattoos are "hidden" because I do not want them to affect my employment possibilities. Unfortunately, it is a sad fact that most office opportunities frown upon tattoos and piercings. I believe that this will one day change, as people with tattoos move up in the world. I also believe that the morals and views of society change often.
I like to use this analogy: less than 100 years ago, white people looked down upon African Americans and immigrants. While this is still occurring today (unfortunately), it is less frequent than before. Just like that, I believe tattoos will eventually become acceptable.