Evolution - "The most popular groupware client for Linux, Novell® Evolution™ integrates e-mail, calendaring, tasks and contact management in one easy-to-use application."
Open Source
Kontact - "The KDE Kontact Personal Information Management suite unites mature and proven KDE applications (called components in the context) under one roof."
Open Source
Mozilla Thunderbird - "Mozilla Thunderbird is a redesign of the Mozilla mail component. Our goal is to produce a cross platform stand alone mail application using the XUL user interface language."
Freeware
Mail Washer - This tool has proved invaluable! Mail Washer allows you to check for e-mail that is waiting for you on the mail server without having to download it, although a preview window is available for you to read the e-mails. The jewel in the crown of this program is that you can choose to bounce e-mail back (as well as delete or add to a blocked list) which makes spammer's think your e-mail address doesn't exist :)
Shareware
PalMail - Great small program for checking e-mail on the server, contains a preview window and a delete options, supports multiple accounts. It's also free and doesn't need to be installed, just place in a Folder and run it!
Freeware
PocoMail - A long time favorite, excellent email program.
See the web site for licensing information.