Mystery and a Moment of Truth
You wouldn't normally expect a film composer to also be a film-editor—those are two totally different skill sets. But John Ottman is both, and he did both for The Usual Suspects.
And Ottman knows his stuff. The Usual Suspects has a straight-up classical score, which totally captures the movie's beguilingly enigmatic vibe.
After scoring Public Access and Suspects, Ottman went on to do a ton of scores for Bryan Singer movies (Apt Pupil, X2, Superman Returns, and Valkyrie) but also for movies directed by other people (The Cable Guy, Bubble Boy, Krampus).
The main theme—called "Theme"—for Usual Suspects plays at the beginning of the movie, and sets the tone for the rest of it, building from a sense of mystery towards a feeling of impending realization.
We don't know what's going on in the movie yet, but it's capturing our sense of wonder—the enigmatic piano leads towards dramatic strings that finally resolve the tension. It makes us feel like something crucial will be revealed, but we'll still be left with something mysterious in the end, something we can still puzzle over—which is exactly what happens.
"New York's Finest" uses clacking percussion (giving us the feeling of a stopwatch countdown) and intense bolts of strings to conjure up suspense as we watch the emerald smuggler arrive in New York. "The Arrests" plays during the arrests scene (who'd have thunk it?) when all the suspects are apprehended. Like "New York's Finest" it also uses percussion to give us the sense that we're marking off time towards a moment when the tension will end—probably with violence.
And then there's "The Greatest Trick"—the piece used in final scene, when Kujan realizes the truth about Verbal's made-up story; it has a Turkish vibe, befitting Keyser Söze's Turkish roots. The strings build and scream dramatically at the point where we see Kobayashi's name on the bottom of Kujan's broken cup.
This is the moment of realization promised in the "Theme" that begins the movie. We know the truth, but we're also left with the mystery about what in Verbal's story was true and what wasn't. This is something the music conveys: we haven't fully escaped the mystery.