The truth is, there is not yet a clear, nationwide legal consensus about whether it is okay to publish arrest records online. Florida, for instance, has notoriously open public records laws, and people in government throughout the state say that sites that display these photos are in the clear. Even if you never spend a day in jail, your mug shot can be displayed months or years after you are arrested.
However, other states like Massachusetts have clearly stated that it is not okay to republish a mug shot. The 11th Circuit court ruled that arrest photos were not in the public domain. But, the 6th Circuit court, which includes Kentucky, Missouri, Ohio, and Tennessee, ruled that they were. And elsewhere, people who have had their criminal records sealed are engaging in class action lawsuits against the webmasters of sites that display mug shots.
To find out whether the site that displays your mug shot is breaking the law, check into your state's public record laws. It may take a bit of research since the precedents have mostly been set in the courts. If you cannot find a case that found that displaying them is an invasion of privacy, there is a good chance that the site is not breaking the law. It would probably also be a good idea to consult your defense lawyer to see if he or she has any information.
Even if the site that displays your photo is not technically breaking the law, you still have options to get the information taken down. In a best-case scenario, simply emailing the webmaster can work. In other cases, it can require the assistance of a reputation management expert. In any case, do not feel that you have to live with this black mark. You have options, and you can clear your name and save your reputation.