The file extension commonly used for a saved individual email message is .eml.
An EML file usually contains the complete message in MIME format: headers such as From, To, Subject, and Date, followed by the message body and any encoded attachments. Because it stores the message in a relatively portable format, many email programs can open or import it, including Mozilla Thunderbird, Windows Mail, Outlook Express, and other clients.
EML is not the same as a mailbox container. Formats such as mbox collect many messages in one file, while Maildir stores messages as separate files inside a directory structure. Microsoft Outlook also commonly uses .msg for individual messages, but MSG is Outlook-specific and is not the general-purpose extension most often meant by this question.
The related .emlx extension is associated with Apple Mail, while .pst is a larger Outlook data-file format that can contain folders, messages, contacts, and other account data.