The music which plays after the army of the West is surrounded in The Return of the King: The Black Gate has opened. Aragorn, the fellowship (minus Sam and Frodo, of course), and the entire military might of men are surrounded. Everyone's looking freaked out. Then, Aragorn simply says, "For Frodo," and the most epic choral rendition of the Fellowship theme kicks in as our heroes charge into battle.
"Aniron" aka "Aragorn and Arwen", by Enya. If you weren't sucked into Middle-Earth before this came on, you are now. One of the most ethereal songs ever written? Possibly.
Very little can beat listening to "Isengard Unleashed" while driving through a forest on a foggy day.
"The Black Gate Opens". Dark and ominous and foreboding and all that, then the short quick wistful Concerning Hobbits when Sam is asking Frodo if he remembers strawberries and it's all so sad, but then! Then the music crescendos and Sam hoists Frodo on his back and it's so very awesome.
Special mention has to go to the music in The Two Towers when the Elves march to the rescue at Helm's Deep. That ethereal, contemplative theme, reworked into one of the most Badass marches ever? Awesome. (Starts at 3:02)
Also for the music that plays at the climax of the Battle of Helm's Deep - with the cavalry charging down the slope towards the black mass of Orcs. "The sun is rising towards the heaven. A beautiful silver waterfall of men and horses will soon sweep away the darkness. We won't ever see its like again. Not like that."
The music that plays when Sam gives his inspirational speech.
Even his evil themes are awesome. The pounding "Isengard/Uruk-hai" music simply screams Badass, and the raucous theme for Mordor is just plain warped, which makes it perfect.
"Concerning Hobbits". That little melody is heartwarming in and of itself.
Every iteration of the Rohan theme is great, but the one that can get to you the most is the last 30 seconds of "The ride of the Rohirrim". An entire nation of horse-riding Badass warriors, saddling up fortherescue? HELL. YEAH. That glorious music with the old recording of The Professor Himself reading that sequence? A mashup just waiting to happen.
More trailer music for Return of the King: The reprise of the Gondor theme Howard Shore arranged based on Siren Cues' "Epicalypse". When a trailer makes you shed Manly Tears over its awesomeness, you know the movie itself will be something special.
The whole trilogy can be considered a Crowning Moment of Awesome for Howard Shore. The man wrote twelve hours of music, much of it involving the entire orchestra, over just three years. And every bit of it was fantastic.
The tear jerker Into the West playing at the credits of Return of the King.
In addition to the Tear Jerker feeling of "Into the West", it's been cited that Fran Walsh, one of the writers for the song, was inspired to write it by Cameron Duncan, a teenaged amateur filmmaker who was dying of osteosarcoma (bone cancer) at the time of filming.
Shore managed to put one of his most tear-inducing, spine-tinglingly beautiful moments about 23 minutes into the Fellowship of the Ring end credits.
In the Isengard theme, they hit the open back of an upright piano with huge chains. That itself is epic.
The song played during the closing credits of The Two Towers: "Gollum's Song" is an incredibly touching and moving piece about none other than Gollum, originally written for Björk and sung by Emilliana Torini. If you didn't feel for Gollum's tragic story before, you almost certainly will after hearing this song.
The Cut Song "Arwen's Song", by... Liv Tyler(!), repurposed as "Houses of Healing", a song about Éowyn, and she definitely has her father's chops... It was replaced by the song "Twilight and Shadow" by Renee Flemming during Arwen's vision in the forest of her future son, which Figwit so rudely interrupts.
In Fellowship, the musical cue that plays when the party first enters Khazad-dûm, found in A Journey In The Dark from 2:05 - 3:20.
"My Dear Frodo". You have this sweeping orchestral opening, brand spanking new graphics for New Line Cinema, the promise of a true epic...and then the music segues into "Concerning Hobbits". Especially notable during the film itself, as opposed to the soundtrack. If that's not a warm welcome back to Middle Earth, nothing is.
The music that plays during the Goblin Chase is a mix of deep sounding drums and heavy chanting that rivals the Bridge of Khazad-dûm scene in Fellowship of the Ring.
The first appearance of the Ring in The Hobbit is heralded by the Lord of the Rings theme, played on a few wavering strings. Not a super bombastic part of the score, but an absolutely prefect moment that sends chills down your spine.
In The Desolation of Smaug, witness the awesomeness of Tauriel's exhilarating new theme dueling with Legolas' theme (a reworking of the classic elven themes heard in LOTR) as they race to the rescue of the dwarves during the barrel-riding scene.
The majestic music that plays during the scene where Thorin and company are led into the Woodland Realm.
The love theme between Tauriel and Kili is simply gorgeous.
Billy Boyd (Pippin) getting the credits song, "The Last Goodbye" from The Hobbit: The Battle of the Five Armies. It plays over a similar credit sequence that ended the LOTR trilogy with each character getting a sketch. Listen closely and you hear that it clearly samples "Into the West" from the end of Return of the King. But whereas "Into the West" had a definite feeling of "This is the end" about it, "The Last Goodbye" somehow conveys the notion of "This was just the beginning" and just makes you want to pull down The Fellowship of the Ring and start watching even if you've just gone through nine hours of The Hobbit.
Sons of Durin, an epic and exciting rendition of Thorin's theme which plays when he and the other dwarves join the battle.
The inspirational and heroic theme of Ironfoot from Battle of the Five Armies.