This is Howard Shore's Magnum opus. It's what distinguishes this movie as more than just a great adaptation. His use of themes to represent not only races and kingdoms but characters, objects (like the One Ring, of course), and even concepts is a level above most movie soundtracks. There are even elements of storytelling through the music!
For example, the first time we hear the theme for Gondor is when Boromir is in Rivendell. Since he's more or less alone, the theme is played by a single French Horn in a somber (almost tragic) style. In Return of the King, we see Minas Tirith, capital of Gondor, in all its glory, and so the full orchestra plays the theme.
One more: As the Fellowship begins to break down, so too does the theme. We go from heroic phrases to shorter, interrupted instances. There's a book about the soundtrack written by Doug Adams. I highly recommend it if you're interested!
I know you said movies, but a soundtrack for a show I'm hooked on currently is Legion (FX/Marvel, on Hulu). The whole entire show has an amazing cast to begin with, but Jeff Russo (Fargo, Star Trek Discovery, more) and Noah Hawley put together one hell of a score. I highly recommend it and the show.
I'm going to reframe this as who I think the best composers are:
Bernard Hermann, Vertigo, North by Northwest, Psycho, etc.
John Williams, E.T., Jurassic Park, Indiana Jones, Star Wars, etc.
Akira Ifukube, most of the Shōwa era Godzilla movies
Shiro Shigasu, Evangelion, Shin Godzilla
As far as new work, I'm partial to Scott Stafford on Ultraman Rising. It came out on Netflix this past June and I was really surprised how good that movie and soundtrack were.
The album has been seen as presaging the dark ambient music genre, and its presentation of background noise and non-musical cues has been described by Pitchfork's Mark Richardson as "a sound track (two words) in the literal sense". -wikipedia
The mood and tone of Eraserhead and its soundtrack were influenced by Philadelphia's post-industrial history. Lynch lived in the city while studying painting at the Pennsylvania Academy of Fine Arts, and was fascinated by its feeling of constant danger; describing it both as a "sick, twisted, violent, fear ridden, decaying place" and "beautiful, if you see it the right way."[8][9][1] Lynch and Splet used avant-garde approaches to recording on the soundtrack; including crafting almost every sound in the soundtrack from scratch using bizarre methods. The ambiance of the love scene in the movie, for example, was produced by recording air blown through a microphone as it sat inside a bottle floating in a bathtub.[10] Lynch and Splet worked "9 hours a day for 63 days" to produce the soundtrack and all of the sound effects in the film. Splet recalls the sound effects Lynch called on him to produce for Eraserhead as "snapping, humming, buzzing, banging, like lightning, shrieking, squealing” over the five years it took to produce the film and its soundtrack. -wikipedia
Rogue One. First time I saw it I was sure no one could hold a candle to John Williams. Then I watched it again and the way Michael Giacchino uses a half-step to underline the theme of hope gives me chills just remembering it.
I was just watching Tenet last night and the music kind of took me out of it sometimes because I was like, “Fuck, that music sounds awesome”, though not sure how well it will stand on its own, I’ve not tried that yet.
Yellow Submarine (I think a lot of people either forget this movie exists, or write it off as a kids movie. You're missing out on a movie that could be considered as revolutionary to animation as the Beatles were to music.)
Back to the Future
The Muppet Movie
School of Rock
Bladerunner
The Matrix
There's probably other's, but that's what immediately comes to mind.
Lots of good ones here, I'll add some that haven't been mentioned: Sahara, Rango, both Sherlock Holmes movies, Scott Pilgrim vs The World, the JJ Abrams Star Trek's, The Incredibles, Godzilla 2014, The Road to El Dorado
When I think of exquisite sound design, two of my favorite movies spring to mind: Stalker (1979) and The Good, The Bad, and The Ugly.
The former has such a subtle soundtrack that it's almost like it's not there, but without it so much of the atmosphere of a movie that is heavily atmospheric would be lost.
The latter is just a perfect western with a perfect western soundtrack. The theme is well known, but L'estasi Dell'oro gives me chills every time it starts playing.
Most people, as evidenced by the comments, don't know the difference between soundtrack and score. Either that or they DO know the difference and are choosing to answer as if they didn't.