Be it a movie, a TV show or a game, the background score, for me is an important part of the experience. If used intelligently, it can add to the tension(horror), or get the blood pumping(action) , heighten the emotions(Drama) etc etc.

So what are your favorite background scores?

1) Rurouni Kenshin OVA: Trust and Betrayal: Anyone who has seen this knows why it comes out on the top for me. It has an overwhelmingly epic feel to it, far surpassing anything else done in anime, and remains my favorite over the years.

2) The Good , the bad and the Ugly/For a few dollars more: Ennio morricone is my favorite movie composer, and the legendary scores hes produced in these movies are instantly recognisable about 40 years later.

3) The Godfather: Nino Rotas score for the movie remains one of the best movie scores till date, has a quality i really am at aloss to put in words, but im sure you understand why it makes the list.

4) The Legend of Zelda LTTP: Koji Kondo has created some of the best music for games, and this might just be the crowning jewel. Special mention of the overworld theme, which really gets you pumped up and ready for the adventure

Metal Gear Solid 3 - Debriefing: The song playing during the end of the game, which brings back all the emotion. I'm feeling like a different person since I finished that game.

No More Heroes - Steel Python: The best boss song ever, this one matches the epic fight with Dr. Peace so well it's almost impossible.

The Legend of Zelda Twilight Princess - Queen Rutela: This is the song playing when Queen Rutela's spirit guides you to the young prince. It gave me the shivers because it reminded me of Ocarina, one of the best games of all time, but better.

Devil May Cry 3 - Devils Never Cry: Suits the harsh fighting perfectly, and is a real pumping song overall.

Atonement - Entire OST: There's not just one song that stands out on the soundtrack to this awesome picture. They all do. Some of the most touching, emotional music I've ever heard.

The Ring - The Well: The movie's theme just strikes the atmosphere so well: sad, beautiful, but creepy.

There Will Be Blood - Convergence: Chaos turned into music. You have to listen to understand.

Tales of Symphonia - Staff Roll: One of the few games that took me upon an emotional journey, and this song was the perfect way to cap it all off. I'm not a big fan of the soundtrack overall (sorry Soriku) because it's always over the top, but this song just hit the spot perfectly.

There's many more that don't come to mind right now. And I agree with you: the soundtrack and background music can really make or break a movie/game/show.

I like anything by Joe Hisaishi. He scores almost everything by both "Beat" Takeshi Kitano and Hayao Miyazaki.

The Oingo Boingo score to the film Forbidden Zone is also flawless.

Angelo Badalamenti did an amazing score for Twin Peaks and some other David Lynch films.

Game-wise: Koji Kondo has never let me down. And I love Donkey Kong Country, Mega Man 2, and Katamari Damacy.

@Rubang
I completely forgot about Hisaishi. My personal favorites would have to be the Laputa and the Nausicaa theme. Sonatine was pretty good also

#4) 2001: A Space Odyssey: The opening part of John Williams' 2001: A Space Oddyssey Theme

#3) Conan the Barbarian: The epic middle part of Basil Poledouris' Prologue / Anvil Of Crom

#2) Jurassic Park: John Williams' Jurassic Park Theme

#1) Barry Lyndon: George Frideric Handel's Sarabande:

Honorable Videogame Mentions:

Mega Man 2 (Nes): This game has plenty of quality tracks composed by Ogeretsu Kun, Manami Ietel, and Yuukichan's Papa

Secret of Mana (Snes): The Opening Theme composed by Hiroki Kikuta

The Legend of Zelda - A Link to the Past (Snes):  My favorite 16-bit game. It has some really good music (Koji Kondo) 

Good Thread BringBackChrono :D

Edit:

I forgot posting a TV show score. My choice fell on..

The Office (UK Original Version) Opening/Closing Credits: Old classic Handbags and Gladrags by Mike d'Abo

I can't really narrow it down to a list their are too many I like, but Ennio Morricone is definitely my favorite movie composer. I think that Once Upon a Time in the West is almost as good as the Good the Bad and the Ugly. I also love the song Chi Mai but I never saw The Professional so I don't know if the rest of the movies score is that good.