Since I got nothing better to do right now, I'm gonna pick some tunes out...
Air - Alone In Kyoto
Might remember it from a certain film

Quite minimal and really beautiful.
The Album Leaf - Wet The Day
Something about this track's melody hits me, as does a lot of TAL's sons. I just find it gorgeous.
Angelo Badalamenti - Twin Peaks Theme
I love Twin Peaks, and god damnit I love the melody in this piece.
Autechre - Nine
From the album Amber, where Ae were a bit easier on the ears Mesmerizing.
Biosphere - Poa Alpina
I love ambient, and this track is utter bliss.
Boards of Canada - Kid for Today
Possibly the most beatiful Boards track, but it's hard to single one out.
Chicane - Halcyon
Always considered this one of the most beatiful trance melodies ever written...
The Dead Texan - Glen's Goo
All of Dead Texan's stuff is beautiful, the melodies in this are so good.
DJ Shadow - Fixed Income
I guess Shadow isn't something you'd immediately associate with "Beautiful" but I find this track is.
Explosions In The Sky - Greet Death
Main riff = win.
Godspeed You Black Emperor
Not gonna list a single track or album since just about every melody they make is beautiful.
Gregor Samsa - These Points Balance
Not a very well known artist, but the melody in this one is special.
Jakob - Solace (Album)
All you post-rockers check this album out. Every track is mindblowing.
Jeff Buckley - Hallelujah
Don't really need to comment
Mono - Lost Snow
Damn powerful, damn beautiful.
Múm - The Land Between Solar Systems
Beautiful Icelandic epicness!
Nick Drake - Fruit Tree
Oceansize - Music For A Nurse
Heard this on some advert a while ago and desperately searched for it.
Radiohead - Reckoner
Could list many, but this being their most recent stand-out beatiful song. Incredible!
Royksopp - Sparks
Melody A.M. rocks. This track is so smooth it's like ear sex.
Sigur Rós - Untitled 4
Hard to pick just one, but I went for this one!
Susumu Yokota - Saku
Japanese ambient eargasm!
Yndi Halda - Illuminate My Heart, My Darling!
To reiterate.
