Outside of scores, though, the Weird Sisters' music is great, "Magic Works" being a perfect slow dance song that sounds like something out of a John Hughes movie from The '80s.
The Order Of The Phoenix
John Williams wasn't the only one who could do Awesome Music for the Harry Potter films. Exhibit A: Nicholas Hooper's "Fireworks". The Harry Potter films have never once had bad music in them. The track on the soundtrack (though sadly not in the cut of the movie) comes complete with electric guitar to show the rebellious rockstars Fred and George are.
The music in the beginning of Half Blood Prince when the Death Eaters fly through London and destroy Diagon Alley along with Millennium Bridge, as well as the music in the slow-motion scene of the photographers taking all the pictures of Harry and Dumbledore. Later on in the film, the panning shot over Hogwarts to Draco in the tower as it snows outside is great, and so is the music at the very end when the trio look out from the tower into the sunset.
"Journey To The Cave". Just this bombastic piece as Harry and Dumbledore arrive at Voldemort's Horcrux cave.
Nicholas Hooper created some amazing music found in a deleted scene from Half-Blood Prince.
The Deathly Hallows Part 1
Alexandre Desplat's score for Deathly Hallows Part 1 has some fantastic moments as well. The music at the very beginning when Hermione erases her parents' memories of her is heartbreaking, and really captures the feel of that scene, impressing upon the audience that this the beginning of the end of the series. The music when we open to Malfoy Manor is very sinister, and the music when just Harry and Hermione are in Godric's Hollow is unlike much of the other music in the series... Desplat uses Spanish guitar. And it is beautiful. Oh, and the music when Bellatrix throws the knife at Dobby as he proceeds to Apparate himself, Harry, and Hermione out of Malfoy Manor, which results in his death upon arrival at the beach is dripping with anticipation. The track during Dobby's death is a definite Tear Jerker.
Another powerful piece, "Procession", is heard in the end-half of Deathly Hallows Part 2 when Voldemort is returning to Hogwarts' courtyard with his remaining followers and Hagrid, who is carrying a seemingly dead Harry. The atmosphere just gives out utter sorrow and hopelessness after the fatal battle.
On the flip side, A New Beginning from Deathly Hallows Part 2 has an ethereal feel that embodies the sound of hope. As Harry and friends look to the future, there is a sense of peace at last.
The uplifting and heroic track during Neville's speech.
"Voldemort's End" is an epic and emotional track that is used during the final showdown between Harry and Voldemort.
Officially unreleased, Bruce Springsteen originally did a song for the first movie's soundtrack that was vetoed due to J.K. Rowling's rule against commercial songs. It took 16 years for the demo recording of "I'll Stand By You Always" to reach the public, but the slow beauty of the track and sense of nostalgia and finality made it worth it.