In our solar system, planetary rings are found around all the giant planets, showing spectacular variety. Jupiter's thin ring system is composed mostly of dust. Saturn's rings are the largest and best studied, and the target of the NASA/ESA Cassini space mission that will begin orbiting Saturn in 2004. Its ring system consists of the broad A and B rings (separated by the Cassini Division) and the optically thinner C and D rings. Outside the main rings are the narrow `braided' F ring and rings E and G. Uranus has ten narrow, sometimes eccentric rings and a family of dust bands. Neptune has three distinct rings (Galle, LeVervier, and Adams); the outermost Adams ring is patchy, with the thicker segments termed `arcs.' All the ring systems have moons interspersed, which sculpt, collect, and release ring material. Moons are the likely parents of the present rings, ground down by meteorites and destroyed randomly to produce the relatively short-lived ring systems. Thus, we observe the natural stochastic results of birth and death processes when we examine the rings closely. Ring systems are relatively nearby and provide a natural laboratory for phenomena in flattened disks, including the nebula around our Sun that gave rise to the planets. Cassini will observe Saturn's rings and the numerous physical phenomena occurring within them close-up from 2004 to 2008, refining and possibly redefining our view of ring physics.