The Open Dynamics Engine is used for simulating the dynamic interactions between bodies in space. It is not tied to any particular graphics package although it includes a basic one called drawstuff. It supports several geometries: box, sphere, capsule (cylinder capped with hemispheres), triangle mesh, cylinder and heightmap.
ODE is a popular choice for robotics simulation applications, with scenarios such as mobile robot locomotion and simple grasping. ODE has some drawbacks in this field, for example the method of approximating friction and poor support for joint-damping.