Warning: Wikipedia contains spoilers
Son of Shmi Skywalker, and with an unknown father (in The Phantom Menace ("Episode I", 1999) Shmi states that he has no father. Some viewers have drawn the obvious narrative parallels to the New Testament stories of Jesus Christ's conception and birth). In that film, he appears as a young child. He is found on Tatooine by Obi-Wan Kenobi and Qui-Gon Jinn, two Jedi, and after his gifts are revealed, Qui-Gon is convinced that Skywalker is the individual told in prophecy that will "bring balance to The Force." After Qui-Gon's death, Anakin is trained by Kenobi as a Jedi - though some of the Jedi have reservations about his character. In the course of events he meets Padme Amidala, at that stage a teenager, with whom he forms a strong bond.
In Attack of the Clones ("Episode II", 2002), Anakin, now a young adult and cocky apprentice Jedi (played by actor Hayden Christensen), again meets up with Amidala, on whom he has developed a massive crush. Assigned to guard Amidala, in conversation he reveals, as well as his affection, a distrust of the political process and his view of the need for one strong leader. After the death of Shmi, freed from slavery and living in the deserts of Tatooine with her new husband, at the hands of the "sand people", Anakin's dark side is more strongly revealed as he slaughters a whole tribe of them in bloody revenge. After losing his right arm in a light saber battle with Count Dooku, the movie ends with Anakin's elopement and marriage to Amidala on Naboo.
Episode III is scheduled for release in 2005. It will complete the three prequels to bring us full circle back to Episode IV, first released in 1977. The as-yet Episode III will bridge the large gap between a young Anakin we leave at the end of episode II and the high-ranking Darth Vader, Lord of the Sith, and second-in-command to the Emperor we meet at the beginning of episode IV. According to lots of post-star wars fiction, he landed in a volcano, and this is what required him to don the famous suit.
In A New Hope ("Star Wars, Episode IV", 1977; this was the first released Episode), Darth Vader, now a cyborg, is the brutal second-in-command of Palpatine, the Emperor of the Galactic Empire. He defeats and kills (at least in body) the now-elderly Obi-Wan Kenobi in a light-saber battle, whilst Luke Skywalker and his motley crew assist Princess Leia to escape with the plans to the Death Star. He then appears again piloting a distinctive TIE Fighter, almost, but not quite, preventing Luke's successful starfighter attack on the Death Star.
Vader confronts Luke again in The Empire Strikes Back ("Episode V", 1980), and Vader tells Luke that he, Vader, is his father. Vader tells Luke to join him. Vader tells Luke that they can destroy the Emperor and rule the galaxy as father and son. Luke refuses to join Vader and escapes. For those interested in the saga, this represented a significant change in direction, as the ultimate symbols of good and evil were now understood to have a deeper connection that would demand some final resolution.
Return of the Jedi ("Episode VI", 1983) sees Vader attempt to persuade Luke to join the Emperor and himself on the "Dark Side of The Force". When that fails, Vader and Luke fight another light-saber battle, Luke refusing to attack Vader and all the while attempting to persuade him to come back to the "Good Side" of the Force. Finally, Vader telepathically examines Luke's mind and realises that Leia is Luke's sister (and thus his daughter), and threatens to turn her to the Dark Side. Luke finally reacts with anger, severely injuring Vader. The Emperor then again beseeches Luke to join the Dark Side, but Luke refuses, and so the Emperor uses the energy of the Force to slowly fry Luke. Vader struggles to his feet, grabs the Emperor (thus further injuring himself from the Force's energy) and throws the Emperor down a hole in the Death Star to the Emperor's death. Nearing death, Vader asks Luke to remove his mask so he can see Luke, for the first time "with his own eyes". Vader dies soon after.
His body is cremated in the manner of a Jedi, and the end of the film Luke sees what appears to be a vision of Anakin (without the artificial body of Vader), Obi-Wan, and Yoda smiling down upon him. Thus ends the six-part saga, with a restored order to the galaxy through the "return" of Anakin back to the good side.
It is also worth noticing that "Vader" is the Dutch word for "father", and it may be tempting to read the character name "Darth Vader" as "Dark Father", a word-play that may well be the root of the Sith title.
See: The Skywalker family