WordPress and the new BuddyPress (forum) are couple of immensely popular open source projects in the PHP web applications world.
BackPress is a PHP library of core functionality for web applications that grew out of the WordPress project.
- User Roles and Capabilities (Permission systems)
- Database connections (across multiple servers and multiple datacenters)
- HTTP Transactions
- XML-RPC Server and Client
- Object caching
- XSS and SQL injection protection, including a variety of powerful escaping functions
- Options management
Look here to get a full list of BackPress features.
PHP world offers a lot of open source libraries that you can leverage to build your web application. But, if you have used WordPress or BuddyPress, you will feel right at home implementing some of the features you have grown to like in WordPress into your own next kickass web application.