Michael Nyman's "The Heart Asks Pleasure First." Many versions have a string section for a small part of it, but this one doesn't. posted by Monsieur Caution at 1:41 AM on April 9, 2011
Plenty of Bill Evans. posted by Beardman at 6:41 AM on April 9, 2011
"Merry Christmas, Mr. Lawrence" by Ryuichi Sakamoto http://www.youtube.com/watch?v=SWuptY2C9Xg posted by dorgla at 6:45 AM on April 9, 2011 [1 favorite]
Perhaps these: "Ashokan Farewell" from the soundtrack to the PBS series "The Civil War",
and "The Sacrifice" from the soundtrack to "The Piano". posted by Ginesthoi at 6:58 AM on April 9, 2011
Nocturne by Robyn Hitchcock, from I Often Dream of Trains. The "prelude" is piano only; the "demise" is piano accompanied by electric guitar. The latter never fails to wedge a thumb firmly into my heart. posted by bakerina at 10:51 AM on April 9, 2011
I wasn't thinking of the Brahms because there was a certain motor element to your examples which these lack, but that's of course a very good recommendation.
If you want to hear this music on pianos for which it was composed, that can open a wholenewworld, too: posted by Namlit at 1:10 PM on April 9, 2011 [1 favorite]
http://www.christopheroriley.com/
He does piano covers of Radiohead songs that definitely qualify as melancholy. I haven't listened to his other work though. posted by anotherkate at 2:50 PM on April 9, 2011
Gymnopédies by Erik Satie is what leapt to my mind right away. Also Tori Amos, but can't think of titles. posted by Ellemeno at 2:53 PM on April 9, 2011
From the Jane Campion film "The Piano" - The Heart Asks Pleasure First. Heh, most of that film consists of melancholy piano music... since it's about a melancholic pianist. You could check out the rest of the film's soundtrack :) posted by aielen at 5:38 PM on April 9, 2011 [1 favorite]
The first song that popped into my head was David Bazan's "Hard to Be" posted by shortyJBot at 7:01 PM on April 9, 2011
posted by Namlit at 1:11 AM on April 9, 2011