The problem is that film music is a very large field, despite that it looks, at the outset, to be fairly small. But consider: films have been around for around a century, and films have had music pretty much the entire time. The world of film music runs the gamut from composers who knew some of the great masters to composers who started their careers in rock bands. Erich Wolfgang Korngold knew Mahler and Strauss; Danny Elfman was in Oingo Boingo. Both are beloved in film music circles, often times by the same fans. There is film music written in the dense German Romantic tradition; there is film music written in the Impressionistic tradition; there is film music written in the atonal tradition; there is film music written in the neo-Romantic tradition; there is film music that draws heavily on jazz or other ethnic musical traditions.
Clearly, then, it would be impossible to distill all of film music down to a single list of ten carefully-chosen scores, and that's not what I'm after here. This list is just a starting point: what I'd recommend to a musically curious person who said, "Hey, what's film music all about, anyway?" This is in no way intended to be a Top Ten Film Scores of All Time, although there isn't a score here that I don't include among my very favorites.
(These are in no special order, by the way. I'm writing them as they come to me.)
1. Vertigo, Bernard Herrmann.
Herrmann is considered one of the greatest of all film composers, and with very good reason. His body of work comprises dramatic music of the highest order. He was especially good at composing music that could sum up, very succinctly, the emotional fabric of a film. Herrmann was Alfred Hitchcock's composer of choice for most of his films. His most famous bit of music is probably the "slashing strings" figure from Psycho, but I choose Vertigo because it's more subtly suggestive of unhealthy and obsessive love. It is lush and sumptuous music that nevertheless fills the listener with a sense of disquiet. This is psychological music of the first order.
2. Casablanca, Max Steiner.
Steiner was one of the foremost composers of what film music fans tend to refer to as the "Golden Age". Why was it golden? Well, in those days, musical literacy was a lot more common than it is now, so the directors and producers could be assumed to know something about music, which meant that they would understand what their composers were talking about, and be more inclined to listen to what they had to say. The idea of a director needling a composer because his score did not reflect the temp-score closely enough would have been laughable. Composers were treated as important members of the film-making team, and the music was generally taken more seriously. (Of course, I also think that the appellation "Golden Age" reflects a certain degree of taste on the part of many listeners of film music, a matter of stylistic preference. Much film music of this period was orchestrally dense in the Germanic symphonic tradition.) Casablanca gives us a perfect example of a filmmaker being able to call on musical literacy that is no longer assumed to be essential to a good education: in the famous scene where Victor Laszlo, incensed that the Germans are raucously singing their German anthems, commands the band at Rick's to play La Marseillaise. Producer Hal Wallis instructed Max Steiner to score this scene for full orchestra, rather than use the scoring for the band onscreen, in order to make the moment that much more iconic. How right he was.
As for Steiner's score to Casablanca, it's a fascinating listen not just because it's a fine, fine score in its own right, but because Steiner is able to create an emotionally and dramatically engaging score mainly using two melodic ideas that aren't his own: La Marseillaise, and the song "As Time Goes By". Steiner employs a lot of minor-key quotes from the French anthem, suggesting that Casablanca is full of French people who can't be free, and of course, "As Time Goes By" is the film's love theme.
Casablanca's score yields yet another of the great anecdotes of luck or fortune that led to the film being as good as it is. Steiner, professional as he was, hated "As Time Goes By", and lobbied hard to have the song tossed aside in favor of something original that he would write. Steiner very nearly got his way, but this would have required re-shooting several scenes, because the song is actually referred to by title in the film's dialogue. Those reshoots were impossible, however, because by this time, Ingrid Bergman had already moved on to her next role and cut her hair very short for whatever that film was. So "As Time Goes By" stayed.
Anyway, Casablanca is valuable to a first-time listener because it's so easy to trace the melodies through it, from beginning to end.
3. Chinatown, by Jerry Goldsmith.
Noir scores of the 40s and 50s tended to be full-orchestra affairs. As fine as they often were, they also tended to be just as lush and Romantic in their sound as a great many other scores of those eras. With Chinatown, however. Jerry Goldsmith wrote a score using a very small ensemble, and he spotted the film sparingly, allowing silence to do its work when it is the best tool used. Chinatown also employs some compositional styles that would have been used by the composers of the period in which Chinatown takes place – prepared piano, atonal effects, and a jazz-influenced main theme, heard during the opening credits played by a solo trumpet.
4. Ben Hur, by Miklos Rozsa.
If there's a film music lover out there who doesn't love at least one score to one of the old Biblical epics, I've yet to meet that person. The large-scale Biblical epics of the 50s and 60s tended to all boast fine scores, and in many cases, the scores outshine the films themselves by their quality. King of Kings, The Greatest Story Ever Told, The Robe -- all films that aren't seen much anymore at all, but their scores are beloved by film music fans of all ages. For my money, Rozsa's Ben Hur score is the very best of this subgenre.
These films all tend to give adjectives like "lush" and "Romantic" a new meaning, and Ben Hur is no exception at all. It features a full-sized orchestra and chorus, and the score plays for well over half of the three-hour-plus film's running time. It's a thematically rich score as well, featuring many themes along its long journey, and it is by turns thrilling, moving, Romantic, and it is especially tinged with a strong spiritual tone, as Rozsa's music is required to suggest the holiness of Christ in a film where Christ is a character who is never seen from the front and never heard to speak. Ben Hur is one of the greatest of all film scores, and it's also one of the most accessible to those who are unfamiliar with film music listening in the first place.
5. The Godfather, by Nino Rota.
Here is a different kind of epic score for a different kind of epic. It is intimate and melodic, as befitting a film whose focus is on a single family and its deeds and misdeeds through several decades. If the score's musical language seems somewhat limited, that is probably by design, as the film's focus itself is intensely limited, with the story involving the Corleones through the years, without ever really acknowledging the outside world. Rota's approach to scoring the film is to infuse each scene with a sense of nostalgia, musically suggesting us the sad passing of an age, even if that age is one of violence and crime and death.
6. The Magnificent Seven, by Elmer Bernstein.
This is, perhaps, the definitive score to a Western. Its sound reflects one of the most influential of twentieth century composers, Aaron Copland, with its thrilling rhythms suggestive of no other place on Earth than the Old West and Mexico, and with its theme, which is one of the most famous melodies ever written for a movie. Bernstein's career spans the same time, almost exactly, as Jerry Goldsmith's, and both composers came of age roughly at the tail end of the "Golden Age". Both then were major composers of the "Silver Age" (which I take to start roughly in the mid-1970s and last until around the early 1990s, although good luck getting filmscore lovers to agree on what the "Silver Age" actually is). And both died just a few years ago, after being active nearly until the end of their lives. Bernstein was nominated for an Oscar just months before his death (for Far From Heaven).
7. Star Wars Episode IV: A New Hope, by John Williams.
Well, duh. But seriously, it's one of the iconic filmscores of all time; it's an outstanding example of a leitmotif-based filmscore; and it's an orchestral masterpiece. Simple as that. (And no, it's not "ripped off from Holst".) Williams has been one of the major voices in film music for the last forty years, and in this score you hear why.
8. Apollo 13, by James Horner.
In the clip below, I link the actual scene instead of the isolated music for the reason that this clip, almost more than any other, illustrates just how the ebb and flow of a well-composed score can propel a film's emotional climate along. This scene, without music, would just sit there on the screen, with certain shots lasting an absurdly long time and others feeling incredibly out of place. The music here starts out solemnly and builds a bit before ebbing back down, and in the seconds before the launch itself, you can hear the music rising and falling, undulating beneath the action, in much the same way that our breath quickens during those final seconds of the countdown before the triumph of the launch itself.
The score uses a Copland-esque sound as well, but in a different way from Bernstein in Magnificent Seven; Horner also supplements his orchestra with synthesizers in nice ways that don't stand out horribly. (I don't think Horner has ever been as good as he was in the mid-90s.)
9. Blade Runner, by Vangelis.
The film is considered by many (not by me, although I do kind of like it) to be a classic, and one of its most defining elements is its score, by Greek composer Vangelis. What's primarily notable is that the score is almost entirely electronic (the only non-electronic thing that I can recall in it is the saxophone in its gorgeous love theme), and it's on that basis that I cite the score here. The world of Blade Runner is one of the most visually amazing in all of film – the visual design has proven to be extremely influential ever since, in the world of science fiction cinema – and Vangelis produces a score that is a perfect counterpart to it. In the sequence below, the main titles and first few visuals from the film, note the way Vangelis chooses to musically depict the future cityscape we first look upon. At the very first glimpse, 2019 Los Angeles looks hellish and dystopian, but the Vangelis music works against that impression, with a synthesized "harp glissando" as the city fades into view, almost musically symbolizing the curtain going up; and note that rather than write grim and dystopic music (the kind of thing that seems to dominate techno music today), Vangelis's music is primarily music of awe. In fact, it's eerily beautiful.
Aside: in searching out that clip, I noticed something interesting. In the clip above, note the "big melody" that is heard at about the 2:58 mark, when we are looking across the city and we cut to the eye of someone looking out over that city. Now watch this clip of the famous "I've seen things" speech by Roy Batty at the end of the movie (particularly starting at about the 2:25 mark). It's the same melody. Is Vangelis telling us that it was Batty's eye we saw back at the beginning of the film, looking out over the city? Are we seeing some of the things that he has seen? This is the kind of thing that paying attention to film music can bring up.
10. Princess Mononoke, by Joe Hisaishi.
Here we have a great example of Japanese film music, as well as music for an animated film. Animated films can rely on their music to a much greater degree than live action, and this is as good an example as I've ever heard – in fact, for my money, Joe Hisaishi is writing some of the finest music for films anywhere today. Music for animated film can sometimes get overlooked, even by film music lovers, for many reasons. Many animated films use songs along the way, and many of the more recent ones are outright musicals, which tend to require different kinds of discussion than "regular" film scores. But musical storytelling is still musical storytelling, and Hisaishi is one of the best.
Pick those up, explore them, and you're well on your way.