Which planets have ring systems?
The outer planets, a.k.a. the gas giants, all have rings: Jupiter, Saturn, Uranus and Neptune, at least at present. Rings, depending on their conditions and origin, may be somewhat unstable and transient, and it is entirely possible that planets will gain or lose rings over their lifetime. For example, perturbations of various moons (such as Phobos) could result in their orbits degenerating, tearing the moon apart and forming a new system of rings, whereas rings could also be dissipated due to similar perturbations, or due to their constituent particles crashing into their planet. There are also likely to be planets among the hundreds discovered by various exoplanet projects which also have rings, although we can't tell for certain at present.
Rings, as they exist in the solar system, are predominantly made of ice and very small silicates, which requires that they are beyond the "frost line," or, the distance from the sun at which solar radiation diminishes to the point that volatile compounds like ice can form. It's entirely possible that ice rings might have existed in the inner solar system before the sun heated to its current temperature, but this would be virtually impossible to empirically test. What is currently possible would be rocky rings, which would probably happen if our moon, either of Mar's moons, or a system of asteroids were shattered at the correct orbital distance from one of the inner planets.
Jupiter, Saturn, Uranus, and Neptune.
Jupiter's ring is thin and dark, and cannot be seen from Earth. Saturn's rings are the largest; they are bright, wide, and colourful. Uranus has nine dark rings around it, and Neptune's rings are also dark, but contain a few bright arcs.