Sajax is an open source tool to make programming websites using the Ajax framework — also known as XMLHTTPRequest or remote scripting — as easy as possible. Sajax makes it easy to call PHP, Perl or Python functions from your webpages via JavaScript without performing a browser refresh. The toolkit does 99% of the work for you so you have no excuse to not use it.
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.
jMaki is an Ajax framework that provides a lightweight model for creating JavaScript centric Ajax-enabled web applications using Java, Ruby, PHP, and Phobos.