I don't really have a vast array of music knowledge at my disposal, focusing instead on the visual facet of art, however I am familiar with a fair number of film composers and scores.
My favourite soundtrack, hands down, is the entire Lord of the Rings trilogy soundtrack by Howard Shore: Complete LOTR Soundtrack. I really don't have words for how some of the music makes me feel. Absolutely amazing in my book.
That said, I do enjoy a lot of others. Some of the ones that come to the top of my head immediately are (in no particular order):
Han's Zimmer:
Pirates of the Carribean Example: Main Theme
Sherlock Holmes Example: Catatonic
This entire soundtrack has such a different sound from typical movie scores. I really like a lot of the tracks.
Inception Example: Time
Joe Hisaishi:
Spirited Away Example: The Sixth Station
I really don't remember most of the music in Spirited Away all that much but I do really like some of it.
Castle in the Sky Example: The Girl Who Fell from the Sky
I really love the example song I listed here (sort of the main theme of the movie).
Yann Tiersen:
Amélie Example: La Noyée
Oddly enough, I haven't even seen the movie. I don't even remember how I found this soundtrack honestly... I just love it. Accordians ftw.
Bruno Coulais:
Song of the Sea Example: Dance With The Fish
I just watched the movie, and let me say, I was blown away. Not only is it a great movie, some of the music is simply enchanting.
John Powell:
How To Train Your Dragon Example: Test Drive
The movie is good, the music is better. So many of the songs in HTTYD are amazing.
Vangelis:
Chariots Of Fire Example: Chariots Of Fire
The theme song is mostly the reason I like this score.
John Williams:
Indiana Jones and the Raiders of the Lost Ark Example: Main Theme
Yep, John Williams had to be here someplace...
Well, those are some of my personal favorites. I might add to this list as I remember more great soundtracks/scores that I love.