In Roman mythology, Nepune was the god of the sea.
After Uranus was discovered, it was noticed that its orbit didn't follow Newton's law. It was then predicted that there must be another planet that was pulling the orbit of Uranus out of wack.
Neptune was observed on September 23, 1846 by Johann Gottfried Galle and Heinrich Louis d'Arrest near where it was predicted indepedently by John Couch Adams and Urbain Jean Joseph Le Verrier. Soon an international dispute between England and France arose over priority and right to name the newly discovered planet. They are now both credited with Neptune's discovery. Observations have shown that if the search for Neptune had been a few years earlier or a few years later the planet wouldn't have been found anywhere near its predicted location because the orbits calculated by adams and Le Verreier diverge from Neptune's actual orbit quiet frequently.
Neptune is composed of various "ices" and rock with approxamately 15% hydrogen and a bit of helium. Unlike Saturn and Jupiter, but similar to Uranus, it most likely to have a small core of rocky material.
Its atmoshpere is primarily hydrogen and helium with small amounts of methane. The blue color of Neptune is the result of absorbtion of red light by methane in the atmosphere.
Neptune also has rings. Observations from Earth show faint rings, but Voyager 2 shows complete rings with bright clumps. One has a curious twisted structure. Like Jupiter's rings, Neptune's are very dark but their composition is not known. The rings have been named:the outermost one is Adams, followed by an unnamed ring that coorbitals with Galatea, then Leverrier, and the faint Galle.
Almost everything we know about Neptune comes from Voyager 2's visit on Augest 25, 1989.
Neptune has winds that can reach 2000 km/hr that are confined to bands of latitude and large storms. When Voyager 2 passed by Neptune, the most prominet feature was the "Great Dark Spot" in the southern hemisphere which is similar to Jupiter's "Great Red Spot". However, Neptune's 700 mph winds blew the spot westward. In 1994, the Hubbles Space Telescope showed that the Great Dark Spot has disappeared!! It has either being covered by other parts of the atmosphere or has dissipated. A few monthes later, the Hubble Space Telescope discovered a new dark spot in Neptune's northern hemisphere. This indicates how turbulent the atmosphere of Neptune is.
Neptune has eight known moons, Triton and seven smaller ones. 
More info on Neptune!!
Learn more about Voyager 2, the only spacecraft to visit Neptune.
Facts on Neptune.
Info from NASA.
Highly recommended Neptune link.
