Moons are `fossils" into a planet's past. The major, named moon systems are:

Earth: Luna (The Moon)

Mars: Deimos, Phobos

Jupiter: Adrastea, Amalthea, Ananke, Callisto, Carme, Elara, Europa, Ganymede, Himalia, Io, Leda, Lysithea, Metis, Pasiphae, Sinope, Thebe

Saturn: Atlas, Calypso, Dione, Enceladus, Epimetheus, Helene, Hyperion, Iapetus, Janus, Mimas, Pan, Pandora, Phoebe, Prometheus, Rhea, Telesto, Tethys, Titan

Uranus: Ariel, Belinda, Bianca, Cordelia, Cressida, Desdemona, Juliet, Miranda, Oberon, Ophelia, Portia, Puck, Rosalind, Titania, Umbriel

Neptune: Despina, Galatea, Larissa, Naiad, Nereid, Proteus, Thalassa, Triton

Pluto: Charon (note: Pluto/Charon form a binary planet, but Charon is the smaller so it is classed as the moon of Pluto)

New, smaller moons are being discovered all the time with recent space missions. The total count of moons (as of 12/18/2001) are:

      Mercury - 0 moons      Mars    -  2 moons   Uranus - 20 moons
      Venus   - 0 moons      Jupiter - 28 moons   Neptune - 8 moons 
      Earth   - 1 moon       Saturn  - 30 moons   Pluto -   1 moon

Moons of Mars:

Deimos

Phobos

We speculate, from their irregular appearances and low mean densities, that Deimos and Phobos, are captured asteroids. Both Deimos and Phobos are saturated with craters. Deimos has a smoother appearance caused by partial filling of some of its craters.

Moons of Jupiter:

Adrastea is a typical small moon

Metis is the innermost known satellite of Jupiter

Amalthea is one of Jupiter's smaller, irregular moons, an example of moon collecting dust from another moon (Io)

Moons of Saturn:

Atlas the second of Saturn's known satellites, orbits near the outer edge of the A-ring

Enceladus is one of the innermost moons of Saturn. Enceladus reflects almost 100 percent of the sunlight that strikes it and has evidence of internal heating and recent resurfacing effects

Epimetheus and Janus are the fifth and sixth satellite of Saturn that share the same orbit, and have a possible origin as single moon that split

Hyperion is one of the smaller moons of Saturn. It has a pock-marked body and is the largest irregularly shaped satellite ever observed.

Iapetus is one of the stranger moons of Saturn, its leading side is dark with a slight reddish color while its trailing side is bright

Dione is the densest moon of Saturn other than Titan, and has several usual characteristics: 1) has a rocky core and ice crust, 2) is heavy cratering on trailing hemisphere, 3) has bright, wispy features

Rhea is the largest airless satellite of Saturn that has different regions with different crater sizes indicating that parts of the moon have undergone resurfacing since formation

Mimas is one of the innermost moons of Saturn with a very large impact crater that came close to fracturing the moon

Tethys is an icy body similar in nature to Dione and Rhea

Phoebe is the last of the known satellites of Saturn and orbits in a retrograde direction (opposite to the direction of the other satellites' orbits) in a plane much closer to the ecliptic than to Saturn's equatorial plane. Thus, Phoebe may be a captured asteroid with a composition unmodified since the time it was formed in the outer Solar System.

Moons of Uranus:

Ariel is a relatively small satellite and is the brightest moon of Uranus

Miranda with a jumbled surface unlike anything in the Solar System, indicates evidence of violent past with possible multiple shattering and reassembly

Titania is the largest moon of Uranus and is marked by a few large impact basins

Moons of Neptune:

Proteus is one of the darkest objects in the Solar System

Triton is the largest moon of Neptune and is colder than any other measured object in the Solar System with tidal heating after formation changed surface