Panda3D offers three built-in choices to use for Physics:

• Panda's Built-in Physics Engine: Panda3D has a very basic physics engine built-in that may apply forces to classes. The physics engine can handle angular or linear forces, as well as viscosity.
• The Open Dynamics Engine: This is a more extended physics engine that Panda3D offers good integration for, you will want to use this if you need more complex physics simulations. In Panda3D versions 1.5.3 and above, this is integrated in the binaries from the download page.
• NVIDIA PhysX: New in 1.7.0. Not yet documented.

When you have a very simple simulation, you will most likely want to use the built-in physics, since this is a much more stable system than ODE, which is still a bit experimental. Although, when the built-in engine doesn't offer enough functionality for you, it is advisable to switch to ODE.

Integration for various other physics engines have been provided by the community on the forums:

• Old wrappers for AGEIA PhysX: http://panda3d.org/phpbb2/viewtopic.php?t=3108
• More recent wrappers: http://panda3d.org/phpbb2/viewtopic.php?p=27906#27906
• Most recent wrappers: http://panda3d.org/phpbb2/viewtopic.php?t=5067
• Wrappers for Newton Game Dynamics: http://panda3d.org/phpbb2/viewtopic.php?t=2617