If you're an administrator, you can use AUTHENTICATE PLAIN to open an IMAP connection to a user account using your password. (Not sure whether any major IMAP clients allow this, though.)
You can save a message to disk by right-clicking on the message entry in the message list view in the web UI, then selecting "Show Original". Form that window, save it to disk.
You can also fetch and store messages via the REST interface. The REST interface is described
in the wiki.