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. See screenshot from here.
RoundCube Webmail is written in PHP and requires a MySQL or Postgres database. The user interface is fully skinnable using XHTML and CSSÃ‚Â 2.