Besides ioquake3, some of the other popular open-source game engines include DarkPlaces (used by Nexuiz / Xonotic), Qfusion (used by Warsow), Cube, Cube 2, Crystal Space, and even the Blender Game Engine, among others. This summer we will hopefully see the open-sourcing of id Tech 4 too.
The r5ge game engine is brand new and written from scratch. It's designed to be a lightweight C++ cross-platform engine. According to its development page, the engine prides itself upon clean, efficient, and easy-to-understand code. Right now the engine is considered to be in an alpha state. The engine includes Linux, Mac OS X, and Windows support at this time.
The project page for the R5 Game Engine is on Google Code. There's also various other pieces of information on the development blog.
Let's just hope yet another game engine project doesn't go the way of the XreaL game engine project, which at first was setting itself up to be the most advanced open-source game engine, and then being adapted to Enemy Territory, but in the end it's largely faded away like so many free software projects.