We can check our email accounts remotely using PHP and its imap functions, which allow us to communicate with mail servers via IMAP, POP3 or NNTP protocols. You can build a PHP mail scriptof your own that will accept an email account, password and optional IMAP port number. In drupal you have few modules available for 5X versions which you can us for integrating email clients with drupal site. Here I will List and discuss most of them.

Roundcube
Roundcube 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..

Features

Multilingual capabilities
Full support for HTML messages
Multiple sender identities
Find-as-you-type address book
Richtext/HTML message composing
Searching messages and contacts
Threaded message listing New!
Spell checking
Extensible using the Plug-in API

You can integrate roundcube with Drupal site.Projects of your interest:-

http://drupal.org/project/roundcube
http://drupal.org/project/rcmail
http://drupal.org/project/webmail
http://drupal.org/project/mailman_api

Roundcube site: http://roundcube.net/