Panda3d is a fully featured 3D engine capable of 3D games or simulations. Written in C++ and Python it possesses the power of C++ and the ease and speed of developing with the Python API. Along side excellent documentation [edit: ok this might be a stretch 
] a vibrant and friendly community is willing to assists with any questions. The engine is under constant development in partnership between Disney, Carnegie Mellon University, and the open source community. The engine currently supports many operating systems and platforms, including the iPhone and browser plugins. All of this with a very liberal BSD style license.
Python
Easy to learn, easy to script, powerful multi-platform language.
Mature
In development since 2001, Includes every thing out of the box.
Just works.
It just works, no crashes, no missing design gaps.
Documentation
Excellent documentation, complete and up to date.
License
Liberal BSD style license, use how you see fit!
Systems
Support for many OSes, including windows, linux, and OS X.
Shader
Automated shader generation.
Animations
Supports joint based animations
Collisions
Support for sphere, tube, or per poly.
Scene Graph
Modern scene graph view.
3d Files
Supports many 3d editors including Max, Maya, and Blender.
Networking
With robust netcode Panda3d has been used for two MMORPGs.
Performance
Its fast, plus profile tools to optimize performance
Debug
Wealth of debug tools and hooks.
Error Handling
Very good error handling and reporting, no segfaults!
Math
Handling of everything from Quaternion to Projection Lens.
Terrain
Geo Mip Map based terrain generation.
Multify
Pack and patch your game using advanced package system.
Physics
Simple native or choice of ODE or PhysX based
Sound
OpenAL, FMod, Miles
Movies
Play movies right in game