The most touching soundtracks.

This

For real though probably Planescape Torment and Bastion.

Braid - Downstream (actually, every song in that soundtrack is perfect ^^)

Bastion.

this

Sniper wolf death scene from mgs1, there's plenty more from that series as well.

Portal 2 has

Triage?

The soundtrack from Kingdom Hearts (slow version). Also Bastion.

Alone in the Dark

http://www.youtube.com/watch?v=nh2kSs89Xxw

Assassin Creed 2 - Ezio's family

Whenever I listen to this song, my mind just recalls the death of his brothers and father.

Besides, there are some more like Final Fantasy X - Suteki da ne, etc.

Pretty much any JRPG OST.

Bastion has a great soundtrack. Not necessarily so touching, but I love the Zelda music

Combo x2

Also

Bioshock Infinite

Mass Effect 3 ending was pretty cool musicwise actually.

But I prefer the Krogan one.

credit song of the walking dead...sob sob.

and sth out of topic, the departure-gattaca OSTa truly magnificent movie with such a set of lingering soundtracks

Silent Hill OST is pure gold. Check "Reprise" and you'll see what i'm talking about.

I don't know if it's "touching" enough, but it's kinda awesome. :)
http://www.youtube.com/watch?v=zEH_LSL4rVw

NieR OST. Beautiful.

Well I played many games with spectacular soundtrack, recently I liked in particular To the moon-For River and Braid - The True Undercurrent

Lisa Miskovsky – Still Alive
was pretty good

Final Fantasy 3 (In North America, 6 elsewhere) Selene's Song, The Opera, and also the Overture. Especially the versions of these done with a real orchestra... One of my favourite games for music!

Might not be my favorite/most touching one, but I like it a lot.

Full Shadow of the Colossus OST

The Walking Dead ;___;