Oh yes... "Storm", by Craig Armstrong: http://www.youtube.com/watch?v=_yZSch47S50

The reason it tears me up is because it's an absolutely perfect song for my Charr Guardian character, Nyrri Silversnow. She is adamant about protecting the innocent, standing up to evil no matter what the odds. She's got a very big heart, and this song suits it beautifully.

It's Alive- Selfless
Song ALWAYS make me get feels ;3;

That's beautiful. And I don't have one that makes me cry, per se, but I do have a few that make me very emotional.

http://youtube.com/watch?v=lC_tfsmdDYo

http://youtube.com/watch?v=OQeFvUuPNHc

Those are two of them :3

http://www.youtube.com/watch?v=WwvQ6Hs7tJE

http://www.youtube.com/watch?v=M5Nt9V0bszE

https://www.youtube.com/watch?v=yIybK0OH2uI

And basically everything James Horner has ever done.

http://www.youtube.com/watch?v=FvDiFkBV744

http://www.youtube.com/watch?v=K8zYrt0c8O4

http://www.youtube.com/watch?v=DSfJoH4L1Cs

"American Beauty" by Thoman Newman:
https://www.youtube.com/watch?v=al21Vtlsg4A

"Viðrar vel til loftárása" by Sigur Rós (not technically minimal lyrically, but most of the song is instrumental + the lyrics are in Icelandic):
https://www.youtube.com/watch?v=_9CPKtDy3fM

I don't know what it is, but a simple piano track backed by a string section always makes me very emotional. These two songs, though, have the unique ability that no others possess of reducing me to a pathetic puddle of tears whenever I listen to them. XD

"Return to Hot Chicken," Yo La Tengo, from I Can Hear The Heart Beating As One (1:43)
http://www.youtube.com/watch?v=QAqfz-MYSlo

"Diamond Claw," Wilco, from The Wilco Book (3:11)
(This song is hard to find, since it was only released with a book of liner notes.)

"Storm," Godspeed You! Black Emperor, from Lift Your Skinny Fists Like Antennas To Heaven (22:38)
http://www.youtube.com/watch?v=61LZKhBgDso

"On the Beach of Dreams - Another World" [also called "Dream of A Shore Near Another World"], Chrono Cross Original Soundtrack (2:22)
http://www.youtube.com/watch?v=ROKcr2OTgws

Goodnight Julia - Yoko Kanno
From: Cowboy Bebop - http://youtu.be/tpGRXCp_BXA (Also adding a link to Space Lion, a similar song that's longer and I feel more somber http://youtu.be/zOH2vWhxO7k )

Road to Perdition (Title Theme) - Thomas Newman
From: Road to Perdition - http://youtu.be/XN3ogbTuDSE

Reprise / Again - Joe Hisashi
From: Spirited Away - http://youtu.be/KgEQNlR4A6o
I often wonder if this one is more situational for myself because the movie struck such a deep cord with me and despite it's less than sad tone, it's this bittersweet tears it brings, IMO.

Samuel Barber - Adagio for Strings (https://www.youtube.com/watch?v=izQsgE0L450)

I'm oldskool tho XD

just gonna say anything from The Fountain's score/soundtrack. It was a painfully beautiful movie and the score goes in line perfectly with that.

full - https://www.youtube.com/watch?v=FHCNtaf2ypY (i couldn't find the one with actual song breaks in it with titles/timestamp cuts :U)

particular emphasis on these 3-
https://www.youtube.com/watch?v=4Xaw08vwnrY
https://www.youtube.com/watch?v=7FDAkpQSJVA
https://www.youtube.com/watch?v=N2pzaKoeXcM