When the center-of-mass between two objects lies outside the surfaces of both objects, you have a "binary" object – and there are binary stars as well as planets and asteroids. It's this trait that makes Pluto-Charon a binary planet, where the Earth-moon pair (with a center-of-mass inside Earth) is not.
Below is a diagram and two movies that show the motion of Pluto and Charon in their orbits. These diagram shows the orientation of the orbits around the time in its 248-year orbit when Pluto was closest to the Sun (in 1989).
Most satellites in our solar system are too small, compared to the planet they orbit, to put the balance point very far from the center of the primary body in the system. But the mass ratio of Pluto to Charon is just 8:1 (compared to typical planet:satellite mass ratios of 10,000:1), and the balance point of Pluto-Charon lies a few thousand kilometers above Pluto, toward Charon.
Although Pluto-Charon is the only recognized binary planet in the solar system, there are binary asteroids and binary Kuiper Belt Objects. Of course, there are also many binary stars in the galaxy as well. New Horizons is expected to be the first mission to visit any kind of binary object.
Click here to make a model of the Pluto/Charon system.