qmailcheck looks for new mail in multiple IMAP mail boxes. If you get a lot of mail and split the messages into separate boxes (typically on the server side using procmail or sieve), then checking all the boxes by hand can be tedious. QMailcheck displays the results in a formatted list, highlighting the newest items. When new mail arrives in a folder, it is capable of raising the window, issuing a system notification, flashing the LED (on phones only), and vibrating (on phones only), all on a per-folder basis.
Trojita is a Qt IMAP email client. It is a pure Qt4 application with no additional dependencies. It has a robust IMAP core implemented using Qt's Model-View framework. Standards compliance is a design goal. It has support for bandwidth-saving mode aimed at mobile users with expensive connections. In addition to the usual SSL/TLS connections, the server can be accessed via SSH. It has on-demand body part loading, offline IMAP support, and safe dealing with HTML mail (actually more robust than Thunderbird's).