RedBean can be integrated in various PHP MVC frameworks. If you are looking for a framework that ships with an integrated version of RedBeanPHP I recommend to take a look at Shozu. Besides Shozu, RedBeanPHP is known to integrate well in Zend Framework, Kohana PHP Framework, CodeIgniter and many more popular frameworks.
While RedBean is a stand-alone library you can get RedBean integrated in an MVC framework as well. The Shozu framework comes with out-of-the-box RedBeanPHP support. Shozu is a very smart and lightweight framework for rapid application development on the PHP platform. Some of the inspiration for Shozu comes from the well known 'green framework'. Shozu is also the first framework that has adopted RedBeanPHP for ORM. It's a framework worth considering!
Valedaemon offers a RedBeanPHP module for Kohana 3. This includes the latest RB package, so it's just fire-and-forget!
Nibble is a light-weight, plugin-based PHP 5.3 framework. Nibble focuses on the use of reusable components (plugins) to allow rapid application development and share code among developers. Nibble ships with RedBeanPHP.
Dashy MVC Framework ships with RedBeanPHP. Dashy is an easy to use, lightweight MVC framework for PHP that plays very well with AJAX.
RainPHP Framework offers out-of-the-box RedBeanPHP integration (as a driver). The Rain Framework for PHP is very well designed modular MVC framwork suitable for any type of application.
Lexa Tools is a modern and liberal PHP 5.3 framework (liberal in the sense that it does not enforce a framework-like structure). You can find more information about this framework on the Lexa Tools website, the code is hosted on Google Code.
Akaikiwi is a lightweight and easy-to-learn PHP framework that ships with RedBeanPHP.
FreeFrame is a lightweight PHP framework to build rich internet applications. This framework ships with RedBeanPHP.
Asar framework is a resource oriented framework for PHP that ships with RedBeanPHP.
RedBeanPHP Easy ORM for PHP © 2014 Gabor de Mooij and the RedBeanPHP community - Licensed New BSD/GPLv2