It's hard to imagine what Star Wars as a franchise would be like without the music of John Williams. George Lucas originally thought of perhaps using classical music like 2001: A Space Odyssey, but quickly realised that the film would need a fully developed score. Thus, the influences of Holst and Stravinsky were swept into Williams' famous score, which extended to the second and third films in the original trilogy. But while Williams' music injected a heady cocktail of swashbuckling and heightened emotions direct into the trilogy's bloodstream, there was a fair amount of score that wasn't used at all.
It's admittedly difficult to look at the trilogy in objective hindsight and decide what should have stayed and what shouldn't, but we'll at least provide the material and the context, and you can decide for yourself. This is not by any means a definitive guide, but more a taste, should people wish to go on and study the scores in further detail.
Star Wars (1977)
This is more an example of evolution than anything else. While the bones of the splendid main title are here, there are differences in the arrangement, notably the swell the cue opens with. This is the first ever recorded take of the Star Wars main title.
Note here, in the final film version, that the orchestral swell has been removed, instead opting for a direct crash in line with the "STAR WARS" title appearing out of nowhere.
One of the more famous changes for the original film. The pivotal scene where Luke looks at the twin sunset (inspiring the oft-used cue title 'Binary Sunset') was originally scored with more dramatic material.
However, Lucas requested it be rescored with Ben Kenobi's theme, foreshadowing Luke's adventure and eventual transformation into a Jedi Knight.
This cue was originally composed for the scene in the trash compactor, where Luke is pulled under by a tentacled monster (the Dianoga of the title), and features at 0.14 a motif that would be used to score the closing walls of the compactor. The final Dianoga scene was unscored, however this cue was featured in the 1997 'Special Edition' for the expanded Mos Eisley approach sequence.
The Empire Strikes Back (1980)
'The Imperial Probe'
Empire opens with an Imperial Star Destroyer releasing probe droids into the far reaches of space in order to find the Rebel base (and by extension Luke Skywalker). The original opening cue was quite different, unleashing a big brass assault and strains of Darth Vader's theme, underscoring Vader's intent on finding Luke.
The final film cue was more subtle, leaving the scene with a more ambient and atmospheric feel with a prominent use of harp, as well as no sign of Vader's theme.
After coming to Luke's rescue, Han Solo himself finds that he needs saving. After they hide in a shelter for the night, Rebel snowspeeders search for the pair. Originally used was a propulsive and distinctive military piece as heard here:
In the final film, this was replaced by looped sections of 'Hyperspace' from the end of the film where the Millennium Falcon escapes from Cloud City.
'The Probe Scanner'
One of the most memorable of Empire's musical scenes involves the introduction of the Imperial fleet under the command of Darth Vader, with the gigantic Super Star Destroyer literally overshadowing its smaller counterparts. For this scene, John Williams composed a specific version of Vader's theme.
However, in the final film much of the cue was replaced by the first movement of the concert version of The Imperial March.
'The Snow Battle'
One of the most iconic moments of Empire is the image of the terrifying AT-AT walkers approaching the Rebel base, and this was another moment that was originally scored. In the film, the cue doesn't pick up until we see the fighter pilots climbing into their snowspeeders, but the complete piece opens with an incredible movement using piano to score the lumbering behemoths. A display of Williams' genius, using an instrument seen as benevolent and calming to score pure fear.
Another moment left unscored in the film was the introduction to Yoda, which Williams scored with a humourous and playful rendition of his theme. Only the climax of the cue is heard in the final film scene.
'Training A Jedi'
For Luke's initial training by Yoda on the swamp planet Dagobah, Williams composed a wonderfully lighthearted and jaunty cue that used Yoda's theme as a base. The cue was excised, probably as it preceded the cave sequence, its tone at odds with the seriousness and dramatic heft of that scene. Nevertheless, the cue has been included on every soundtrack album release of Empire since.
'Luke Pursues The Captives'
While in the final film it's virtually silent until the fight in the gantry, the big climactic duel between Luke and Vader was originally fully scored. This section again uses Yoda's theme which, according to the original soundtrack LP, signifies Luke using Yoda's teachings to assist in his fight.
Return of the Jedi (1983)
'Vader Contacts Luke'
In terms of deleted scenes, Jedi had quite a hefty amount excised. One of these was at the beginning of the film, after Vader has arrived at the Death Star. Vader retires to his meditation chamber and searches through the Force to find Luke, who is on Tatooine busy constructing a new lightsaber and concocting the final stages of the plan to rescue Han from Jabba the Hutt.
After Luke kills the Rancor monster, he, Han, and Chewie are sentenced to death and are taken to the Pit of Carkoon where they will be thrown into the belly of the Sarlaac. Williams' original cue for this battle scene was less reliant on previous material, perhaps the reason for its removal.
The final film version of the cue is very much based on Luke's theme and recalls the Death Star music from the original Star Wars.
'The Emperor Arrives'
The original cue was not hugely different, save for a distinctive brass fanfare that served as a bridge between the fierce renditions of Vader's theme.
In the final film version, an insert was used that instead utilised the bridge portion to build to the rendition of the march.
'Ben And Luke On Log'
After Yoda's death on Dagobah, Luke is visited by Ben's spirit who tells him about what really happened with his father. In the film, the scene has no score until Luke guesses who his sister is (where Princess Leia's theme is used), but Williams originally scored the entire scene. And yes, the actual cue title is 'Ben And Luke On Log'.
'Funeral Pyre For A Jedi'
Originally, the scene where Luke burns the battered armour of Darth Vader was scored by a more developed and complex version of Ben Kenobi's theme aka the Force theme.
However the final film version is simpler and perhaps more pure, serving as a bookend of sorts to Luke's character arc with the twin sunset scene.
The Ewok celebration cue - aka 'Yub Nub' - is the one exception here, having originally appeared in the film before being excised from the 1997 edition and every other thereafter. While the actual film version of the cue has never been released, this is the final section of the soundtrack album version, which ended the original version of the Star Wars trilogy.