Not too long ago almost any medium to large size company had strict no-tattoo dress codes. Only recently have tattoos become more mainstream and some companies are beginning to change their policies to allow some ink to show.
The question must be asked: Are tattoos unprofessional?
The obvious next qualification is whether the tattoo is offensive or derogatory. While some may say that this is subjective, common sense can dictate whether a tattoo will offend the majority of people. Tattoos with vulgar language or scantly clad women would likely be perceived as offensive to the majority of the population. Tattoos such as these will likely not be allowed at many companies, especially at higher level roles. That is not a judgement on the person with the tattoo, but is a reflection of cultural and moral norms in our country. Of course those norms may vary based on the industry one's company is in.
Many employees have small, simple tattoos of a symbol, name, or word. Tattoos like these are more likely to be viewed without reaction by the majority of the population. An exception to this would be if the tattoo was on an obvious body area like the face or neck. A small symbol on the inside of the wrist or a small name on the forearm may get a pass by many employers.
While our culture is becoming more accepting of tattoos, many companies still have varying tattoo policies. The best measure of determining whether a tattoo may be overwhelming or offensive is common sense. It is typically best to practice courtesy and err on the side of caution by covering any ink when first beginning a job. Your boss will appreciate your thoughtfulness and professionalism. After job interviews are complete and you have an acceptance letter, find time to have an honest conversation with your new manager or HR rep to determine whether your tattoo is considered "professional" or against policy. Whatever their determination, try to accept it or work with them to find middle ground where the tattoo is covered in certain circumstances and visible where appropriate.