How to use rigidbody simulation for animation? I want to be able to add rigid body physics to my gun when my animation character dies so the gun will drop smoothly, because it is hard to animate things dropping in small areas.

I am not making a game, therefor I do not need to use the game engine instead of cycles or blender render.
As of Blender 2.66, you can press Rigid Body in Properties > Physics.

To enable and disable control of the rigid body with the animation system, keyframe the Animated checkbox.

See the wiki for documentation.