Oh lawd, got a longass list of those.
Namely, everything by Sigur Ros, most stuff by Johnny Cash starting from the American recordings and everything of his released thereafter, just about everything by Mogwai, lots of stuff by The Church, lotsa This Will Destroy You, everything by Explosions in the Sky, everything by Jonsi and Alex, and a handful of songs by Train. But, for sake of brevity, the list of ten, in no order other than grouped by artist:
Svefn-g-Englar by Sigur Ros. [http://www.youtube.com/watch?v=8L64BcCRDAE] (this is definitely my #1 if I had to pick)
Hoppipolla, also Sigur Ros. [http://www.youtube.com/watch?v=_EyI4p0yjDQ] (watch the video for this if nothing else on this list)
We're No Here by Mogwai. [http://www.youtube.com/watch?v=yROEbbe9yxM] I grant this is more of the sad-beautiful.
Auto Rock, also Mogwai. [http://www.youtube.com/watch?v=jLFd6k1BHDk]
You Are My Sunshine by Johnny Cash. [http://www.youtube.com/watch?v=FQ9oIIzMrlA]
Happiness by Jonsi and Alex. [http://www.youtube.com/watch?v=X4j-4FElT8E] If you like this, look up the rest of their stuff. Chances are you'll lost just about all of it.
The Only Moment We Were Alone by Explosions in the Sky. [http://www.youtube.com/watch?v=nzj-ksNOMfU] Only because I can't really post a link to "the entire album", which is so much awesomer than any one song on it, and god damn is that a feat.
The Birth and Death of a Day, also Explosions in the Sky. [http://www.youtube.com/watch?v=ltQqPJ5A2BI] Different album than the last.
Drops of Jupiter by Train, [http://www.youtube.com/watch?v=7Xf-Lesrkuc] because if you don't like this song you are not a human being. Or are a Juggalo. Or a complete and total metalhead.
When I Look to the Sky also by Train. [http://www.youtube.com/watch?v=KipSEcE6gGM&playnext=1&videos=ftoo8qk0y_w&feature=artistob]
So there's my representative ten (not quite "top ten"). Enjoy.
ADDENDUM AND A BIG ONE: Gondola no Uta, [http://www.youtube.com/watch?v=uVYKroONpZI] specifically the rendition of it in Akira Kurosawa's Ikiru. It's a sad but beautiful song, and in the film it gains a new level. Sorry about the quality on the video, it's the only one I could find of the movie's version of the song.