I'm not sure what level of integration you are looking for with cPanel, but there are a few really good linux webmail packages available.
RoundCube Webmail is a browser-based multilingual IMAP client with an application-like user interface. It provides full functionality you expect from an e-mail client, including MIME support, address book, folder manipulation, message searching and spell checking. RoundCube Webmail is written in PHP and requires a MySQL or Postgres database. The user interface is fully skinnable using XHTML and CSS 2.
http://www.roundcube.net/
Zimbra is open source server and client software for messaging and collaboration - email, group calendaring, contacts, and web document management and authoring. The Zimbra server is available for Linux, Mac OS X, appliances, and virtualization platforms. The Zimbra Web 2.0 Ajax client runs on Firefox, Safari, and IE, and features easy integration / mash-ups of web portals, business applications, and VoIP using web services.
Zimbra has an open source and paid versions available, depending on your needs.
http://www.zimbra.com/
Scalix Web Access provides popular and familiar desktop-like features including a three-pane user interface, pull-down menus and right click and mouseover capabilities. Users can drag-and-drop messages, meeting appointments and contacts exactly the same way they do in their desktop mail client. Users familiar with Microsoft Outlook will be immediately productive with Scalix Web Access, without the need for any training.
http://scalix.com/
I hope this helps your search.
