Quite a few of the musical cues in this film would go on to become Star Trek staples. The "Klingon Battle Theme" from the start would go on to become the primary Klingon theme (and Worf's leitmotif), several of the major musical cues would be referenced again and again in later works... and oh yeah, the main theme to the movie became the theme song for Star Trek: The Next Generation, was used as the closing theme for some of the TNG movies, and was also recycled as the opening theme for Star Trek V: The Final Frontier.
The film score received an Oscar nomination, and one of the most beautiful pieces from the film, "Ilia's Theme", is all but forgotten by most non-Trek fans. In fact, it was played as an overture over a black screen before the film began (much as Ligeti's "Atmospheres" played before 2001: A Space Odyssey.)
The soundtrack of Star Trek: First Contact, which Goldsmith also scored, contains what might have been either a Brick Joke, Mythology Gag, or even unrealized Foreshadowing at the end of the main title: the moment that the Borg Cube appears on screen, the same harsh chord that is played over establishing shots of V'Ger can be heard.
"The Enterprise," the stunning cue that plays during the "Kirk looks at the Enterprise for a thousand years" scene, is a Moment of Awesome for both Jerry Goldsmith and the orchestra itself—scoring sessions generally require multiple performances of a track, but they nailed it on the first take.