Mailpile
From Just Solve the File Format Problem
Mailpile is a web-server-based e-mail client under development as of 2013, with the aim of "taking e-mail back" by remedying the deficiencies of other mail clients and webmail services, in particular integrating encryption and privacy services.
It was funded through an Indiegogo campaign, and is free, open-source software. An online demo site is live to test it out, as well as downloads of the installable version (still in an early, buggy alpha stage).