The most touching soundtracks.

Deus Ex: Human Revolution

Hans Zimmer - Insertion (Crysis 2 Soundtrack) ftw.

To the moon.

http://www.youtube.com/watch?v=LvEXqjnuQww

Can't think of anything else but Ib - Memory

Edit: Im stupid so i dont know of to make text a link, here you go: www.youtube.com/watch?v=BbOnvj9wZKc
Shadow of the Colossus - the opened way

To the moon - For River (damn ninjas cutting onions)

Cid's Theme from Final Fantasy 7 Sit down and take your goddamn tea! XD

not really a soundtrack, but this Dead Space Twinkle Twinkle Little Star

Believe Me from Steins;Gate.

This is the thing that still gives me shivers when i remember
http://www.youtube.com/watch?v=5n5R7GaoyGE

Outlaws
and +1 to Bastion and maybe DX:HR
Also, the first Halo.

Xenosaga Episode III
Febronia #2
The Harsh Truth
Hepatica #3 ~ I Believe In You
When The Grief Lets You Go #2

Bastion, especially the songs with lyrics.

GAME, Y U SO SAD?!?!?

Infamous 2

Metal Gear Series have some great tracks. Enclosure and The Best Is Yet To Come. Not to forget about masterpiece - Snake Eater Intro. Oh yeah, and this awesomeness. But enough Metal Gear.
Lost my Pieces from Toradora is one of my favourites too.
Same goes for Blue for Cowboy Bebop.
Lullaby for you from The World Ends With You sends chills down my spine quite often too.

Xenogears
Shin Megami Tensei
.Hack//IMOQ

The soundtrack of the video games are really fantastic and it just made me want to play more.

I thought Terry Cavanagh's Don't Look Back had some really immersive sadness to it, only through its soundtrack.

Bastion, Mass Effect 3, and To the Moon come to mind.

It bugs me that I can't really think of any game scores that have impacted me the same way as film/TV scores have (at least not in the more somber emotional spectrum). I'll have to think on that, but for now, here are a couple that immediately come to mind:

Inama Nushif from Brian Tyler's Children of Dune score. The miniseries provides context, but to really understand that imagery you need to read the books. Profound, tragic, and heartbreaking. Link is to a non-montage version to avoid spoilers.

The Gift of Mortality from James Horner's Bicentennial Man score. So moving, especially in the unspoken subtext of the story.

Final Fantasy 7 soundtrack and the four original .Hack games.

They are bestest.

overall favorite: "Aerith' Theme" by Nobuo Uematsu. (FFVII)

but of the game tracks, that i've stumbled upon lately, it's definately "Brandon 2" by bXmMusic. (Cry of Fear)

any Pantera song

The one I've most recently listened to is Midna's Lament from Twilight Princess. A great piece, the only bad thing about it is how badly Nintendo screwed up the implementation. The section of the game it is in fits the song perfectly, but it's screwed up because you're running through enemies that keep interrupting Midna's Lament with the "battle music".

Ave Maria from Hitman Blood Money, it gets you right in the mood to finish a level perfectly & it really enhances the final scene.

Leaving Earth was very touching indeed.
Though An End Once and for All will always be the best in my opinion.