Mutt is a "small but very powerful text-based mail client for Unix operating systems". It is my current mail client, and my favorite so far, for several reasons.
First, mutt is simple. It's text-based, which makes it a breeze to run over ssh; it includes only email features--no calendar, no to-do list, no other useless PIM features--so it's easy to use and streamlined.
Second, mutt is insanely flexible. It supports a bunch of mailbox formats (mbox, mmdf, mh, and maildir), as well as a bunch of remote mail protocols (POP3, POP3+SSL, IMAP, IMAP+SSL), and allows flexibility in moving messages between these folders (it doesn't assign explicit meaning to any folders unless you ask it to). One major feature contributing to mutt's flexibility is patterns, which allow you to select messages based on many different criteria. Once you have a pattern, you can use it to colorize, score, or automatically process messages.
Like many Unix mail clients, mutt doesn't give you everything in one package. If you want to read HTML mail, you need a text-mode web browser. If it's listed in mailcap, mutt will automatically use it. If you want to send mail (!) you need a MTA. One good choice is msmtp, which is a mail sending program that is as simple and flexible as mutt. Mutt also can't receive mail by itself, unless you point it to a POP3 or IMAP mailbox. I recommend Fetchmail to download your mail and Procmail to sort, filter, or otherwise play with your mail. Mutt shines as an email reader, and integrates wonderfully with the additional tools necessary for email use.
Related: Sylpheed, a GTK+ mail client. Sylpheed is a full-blown GUI mail client, but is still very fast, and has a similarly great set of features like mutt.