Abstract Mercury, Earth, Jupiter, Saturn, Uranus, Neptune, and the moon, Ganymede, have presently-active internal dynamos while Venus, Mars, at least two of the Galilean moons, the Earth's moon, comets and asteroids do not. These active dynamos produce magnetic fields that have sufficient strength to stand off the pressure of the exterior plasma environment. Because of changes in these exterior plasma environments these magnetospheres are very dynamic. The jovian magnetosphere includes a strong time-varying energy source that adds to the dynamics of its magnetosphere and produces a quite different circulation pattern than that found at Earth and, presumably, Mercury. Not only intrinsic planetary magnetic fields produce magnetospheres but also unmagnetized planets. Venus, Mars and comets have induced magnetospheres associated with the solar wind interaction with their atmospheres. Cometary magnetospheres, parts of which can be remotely sensed, exhibit spectacular disruptions called tail disconnections. Even the atmosphereless bodies with weak magnetic fields can interact with the solar wind. Small magnetic anomalies on the moon and possibly asteroids cause weak deflections of the solar wind. The dynamics of these various magnetospheres provide a rich spectrum of behavior which we review herein.