There is a lot of confusion about whether it is illegal under federal law to open mail addressed to someone else. There is also confusion about what the remedies are if your mail is opened. The short answer is that is it illegal to open mail addressed to someone else only in very limited circumstance.
The federal statute that applies to this situation is 18 USC Section 1702. This statute is part of Chapter 83 of Title 18 of the federal code, which is concerned with crimes involving the U.S. Postal Service. This section is called Obstruction of Correspondence.
When It Is Illegal
Under this statute it is only illegal to open mail addressed to someone else if you have taken it from the custody of the Postal Service. That means it is a crime to take a letter, package, postcard, or other item of mail from a Post Office, a mailbox of any kind, or from a postal carrier before the mail has been delivered, if you intend to prevent the mail from being delivered, pry into it, embezzle money, or destroy the mail. The statute is essentially about stealing mail from the Post Office.
There is a common misconception that it is illegal to open mail addressed to someone else that has been delivered to you. There is no federal statute that prevents you from opening mail not addressed to you once it has been delivered by the Postal Service. If you take something that was in the mail you might violate a state law against stealing. If you use information contained in the mail for a wrongful purpose like identity theft, you are breaking state and federal law, but opening the mail is not illegal in itself.
Anyone who steals mail in the custody of the Postal Service or destroys it can be fined and imprisoned up to three years under 18 USC 1705. The person whose mail was taken, opened, or destroyed does not have the right to decide when this crime will be prosecuted. It is up to the federal prosecutor in the place where the crime occurred to decide when, or if, to prosecute and what penalties to seek.
The person whose mail has been taken, opened, or destroyed in violation of 18 USC Section 1702 cannot get civil damages just because the law was broken. The federal statute does not have any civil penalties. If the victim suffered monetary damages because of the federal crime, then that person may be able to sue for damages under state law.