According to NakedSecurity, reading another person's email is a crime that falls under Title 18 of the United States Code (USC) Section 1030. It is classified as fraud and related activity in connection with computers.
As ArsTechnica explains, reading a person's email without permission is a grey area as far as the law is concerned. The Stored Communications Act technically governs the legality of accessing emails stored online, and in 2012, the South Carolina Supreme Court ruled that cloud services, such as Gmail or Yahoo Mail, do not meet the definition of electronic storage as written in the statute. However, the Computer Fraud and Abuse Act states that a person may still be held liable in a situation where they have read the email of someone else.