Mutt supports four authentication methods with IMAP servers: SASL, GSSAPI, CRAM-MD5, and LOGIN (there is a patch by Grant Edwards to add NTLM authentication for you poor exchange users out there, but it has yet to be integrated into the main tree). There is also support for the pseudo-protocol ANONYMOUS, which allows you to log in to a public IMAP server without having an account. To use ANONYMOUS, simply make your username blank or "anonymous".
SASL is a special super-authenticator, which selects among several protocols (including GSSAPI, CRAM-MD5, ANONYMOUS, and DIGEST-MD5) the most secure method available on your host and the server. Using some of these methods (including DIGEST-MD5 and possibly GSSAPI), your entire session will be encrypted and invisible to those teeming network snoops. It is the best option if you have it. To use it, you must have the Cyrus SASL library installed on your system and compile mutt with the --with-sasl flag.
Mutt will try whichever methods are compiled in and available on the server, in the following order: SASL, ANONYMOUS, GSSAPI, CRAM-MD5, LOGIN.
There are a few variables which control authentication: