Moons
Moons:
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 system, 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 range in shape from highly irregular to spheres.  Their shape reflects their formation history, irregular objects are ill-formed moons (captured asteroids or comets) or pieces of a larger moon, spherical objects were once molten spheres, probably at the time of their formation.
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:
Jupiter has 63 confirmed moons as of Jan 2009, i.e. moons with known orbits around Jupiter.  Eight of these moons are regular, meaning they have prograde, nearly circular orbits.  They are composed of the four Galilean satellites, plus the inner or Amalthea group:
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)
The remaining 55 moons are irregular, they have a mixture of prograde and retrograde orbits with high inclinations and eccentricities.  Jupiter's regular satellites are believed to have formed from a circumplanetary disk, a ring of accreting gas and solid debris analogous to a protoplanetary disk.
The irregular satellites are substantially smaller objects with more distant and eccentric orbits. They form families with shared similarities in orbit (semi-major axis, inclination, eccentricity) and composition; it is believed that these are at least partially collisional families that were created when larger (but still small) parent bodies were shattered by impacts from asteroids captured by Jupiter's gravitational field.
Moons of Saturn:
The moons of Saturn are numerous and diverse, ranging from tiny moonlets less than 1 kilometer across to the enormous Titan, which is larger than the planet Mercury. Saturn has sixty-two moons with confirmed orbits, fifty-three of which have names, and only thirteen of which have diameters larger than 50 kilometers.  Saturn has seven moons that are large enough to become spherical.
Twenty-four of Saturn's moons are regular satellites; they have prograde orbits not greatly inclined to the Saturn's equatorial plane. These include the seven major satellites, four small moons which exist in a Trojan orbit with larger moons, two mutually co-orbital moons and two moons which act as shepherds of Saturn's F Ring. Two other known regular satellites orbit within gaps in Saturn's rings. The relatively large Hyperion is locked in a resonance with Titan. The remaining regular moons orbit near the outer edge of the A Ring, within G Ring and between the major moons Mimas and Enceladus. The regular satellites are traditionally named after Titans and Titanesses or other figures associated with the mythological Saturn.
The remaining thirty-eight, all small except one, are irregular satellites, whose orbits are much farther from Saturn, have high inclinations, and are mixed between prograde and retrograde. These moons are probably captured minor planets, or debris from the breakup of such bodies after they were captured, creating collisional families. The irregular satellites have been classified by their orbital characteristics into the Inuit, Norse, and Gallic groups, and their names are chosen from the corresponding mythologies. The largest of the irregular moons is Phoebe, the ninth moon of Saturn, discovered at the end of the 19th century.
The rings of Saturn are made up of objects ranging in size from microscopic to hundreds of meters, each of which is on its own orbit about the planet. Thus, a precise number of Saturnian moons cannot be given, as there is no objective boundary between the countless small anonymous objects that form Saturn's ring system and the larger objects that have been named as moons.  At least 150 moonlets embedded in the rings have been detected by the disturbance they create in the surrounding ring material, though this is thought to be only a small sample of the total population of such objects.
Daphnis drifts through the Keeler gap
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
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:
Uranus, the seventh planet of the Solar System, has 27 known moons, all of which are named after characters from the works of William Shakespeare and Alexander Pope.  William Herschel discovered the first two moons, Titania and Oberon, in 1787, and the other spherical moons were discovered in 1851 by William Lassell (Ariel and Umbriel) and in 1948 by Gerard Kuiper (Miranda). The remaining moons were discovered after 1985, either during the Voyager 2 flyby mission or with the aid of advanced Earth-based telescopes.
A montage of Uranus' large moons and one smaller moon: from left to right Puck, Miranda, Ariel, Umbriel, Titania and Oberon.
Uranian moons are divided into three groups: thirteen inner moons, five major moons, and nine irregular moons. The inner moons are small dark bodies that share common properties and origins with the planet's rings.
The five major moons are massive enough to have achieved hydrostatic equilibrium (they were once molten spheres), and four of them show signs of internally driven processes such as canyon formation and volcanism on their surfaces.  The largest of these five, Titania, is 1,578 km in diameter and the eighth-largest moon in the Solar System, and about 20 times less massive than Earth's Moon.  Uranus's irregular moons have elliptical and strongly inclined (mostly retrograde) orbits at great distances from the planet.
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:
Neptune has thirteen known moons, by far the largest of which is Triton, discovered by William Lassell just 17 days after the discovery of Neptune itself. Over a century passed before the discovery of the second natural satellite, called Nereid. Neptune's moons are named for minor water deities in Greek mythology.
Unique among all large planetary moons, Triton is an irregular satellite, as its orbit is retrograde to Neptune's rotation and inclined relative to the planet's equator. The next-largest irregular satellite in the Solar System, Saturn's moon Phoebe, is only 0.03% Triton's mass. Triton is massive enough to have achieved hydrostatic equilibrium and to retain a thin atmosphere capable of forming clouds and hazes. Both its atmosphere and its surface are composed mainly of nitrogen with small amounts of methane and carbon monoxide. Triton's surface appears relatively young, and was probably modified by internally driven processes within the last few million years. The temperature at its surface is about 38K.
Inward of Triton are six regular satellites, all of which have prograde orbits in planes that lie close to Neptune's equatorial plane. Some of these orbit among Neptune's rings. The largest of them is Proteus.
Neptune also has six outer irregular satellites, including Nereid, whose orbits are much farther from Neptune, have high inclinations, and are mixed between prograde and retrograde. The two outermost ones, Psamathe and Neso, have the largest orbits of any natural satellites discovered in the Solar System to date.
Proteus is one of the darkest objects in the Solar System