BigBlueButton is an open source web conferencing system that enables universities and colleges to deliver a high-quality learning experience to remote students.

Mibew Messenger (also known as Open Web Messenger) is an open-source live support application written in PHP and MySQL. It enables one-on-one chat assistance in real-time directly from your website.

SlimStat is a simple but powerful web analytics program.

An open source Q&A(question and answer) eco-system

stackoverflow-like app written in ruby, mongomapper and mongodb Question answer script.

Digistore Ecommerce 4.0 is a fully featured open source ecommerce solution based on the popular osCommerce engine. Boasting improvements both to the administration and the end user experience - Digistore has quickly become a popular choice for people wishing to market products online.

webpraca is a opensource job board. It's purpose is to provide a way to quickly and easily host a niche job board.

PHP RSS Reader comes with a complete admin panel where every setting can be controlled.The application creates SEO-friendly URLs for every category & article which is important for anyone who will use PHP RSS Reader for creating a feed-based website rather than using it as a personal feed-reader.

Todoyu is an open source task/project management, time tracking & collaboration application that is built with PHP. The application has a modern, Ajaxed interface where both users & clients can have roles on projects.

The Ajax Availability Calendar is a php script designed to show availability of whatever you might need it for (eg. holiday cottage, hotel rooms etc.). 
Free to use on your website or application and is currently being used (v.2) by hundreds, if not thousands, of websites around the world.