RoundCube Webmail is an open source browser-based multilingual IMAP client with an application-like user interface. It is developed in PHP and comes with a very comfortable installer interface.
The configuration took me just about 5 minutes and the webmailer was up and running on my Knoppix Linux box at home.
In the past I tried different webmailers on my local linux box (including AtMail and Claros Intouch). None of them were able to cope with nested folders on my dovecot imap server. RoundCube has no problems with that.
The web interface is very intuitive and uses a lot of AJAX (e.g. drag and drop). So if you would like to have a good looking, modern webmailer try RoundCube Webmail.