One of the famed bits of Star Wars lore is all the deleted scenes from the first three films, few of which have ever seen "official" light of day. Most notorious of these are several scenes from the first act of A New Hope that establish Luke Skywalker's character quite a while before the point where we meet him in the finished film.
He's in the "fields" of his farm, working on a malfunctioning evaporator unit when he looks up and sees flashing lights in the sky. Using his binoculars, he sees a space battle taking place (which we know to be Vader's Star Destroyer pursuing Princess Leia's blockade runner). Then he goes to Toshi Station (where he'd later wish to go to "pick up some power convertors") to let all his friends know about the battle, where he meets his old friend Biggs, who had left the year before to go to the Imperial Academy. Biggs, though, has other plans: he's going to join the Rebel Alliance. Luke, however, is despondent that he'll never leave Tatooine.
Later on, of course, Luke meets Biggs as he suits up with the Rebel pilots to attack the Death Star. A portion of the scene at the end of the film was restored for the Special Edition in 1997, but the earlier Tatooine stuff was left out of the movie. In truth, that's a wise narrative choice, but it's still cool to see those deleted scenes on the Web.
The best of these is this trailer to a projected called Deleted Magic, which purports to be a feature-length "research film" comprising deleted scenes, unfinished sequences, and alternate takes from the original trilogy. Being a trailer, it's meant merely to whet the appetite, and that it does. But it's still cool to see a bit of what might have been (Han telling Leia that she should "wear girl clothes more often"), and it's supremely funny to hear David Prowse reading Darth Vader's lines before James Earl Jones could be dubbed in.
Apparently the entire Deleted Magic project can be found here when their bandwidth isn't getting hammered. I plan to check it out as soon as I am able. I'd frankly like to see Darth Vader's attempt to telepathically contact Luke at the beginning of Return of the Jedi....