I also love melancholy, sad music. Or not even that, just often I find myself to music that's, as mentioned before, dissonant, in minor keys, and downtempo. I love all sorts of music, but that's usually the stuff I get a musicgasm from (although downtempo is a bit more optional, I often get the same kinda pleasure from death metal or other uptempo types). Something about that enchanting bittersweet shade of music just grabs me. I'm a big fan of the blues, but like someone mentioned, while the lyrics are often dark or sad, the music isn't always as low, more often the blues strike me as a happy genre (even if it's just laughing at how goddamn cruel life can be).
Some of my favorite examples are:
The triple combo of "Disposition", "Reflection", and "Triad" by Tool
"Insomniac Olympics" by Blockhead
"H" by Tool
"Run Honey Run" by Morcheeba & Bradley
"Ases Tod (The Death of Ase)" from the Peer Gynt suite by Edvard Grieg
"Perfect Disguise" by Modest Mouse
This one is Love Scene from Zabriskie Point by Jerry Garcia. The first time I heard it and every time since it just grabs me. It's melancholy, playful, sweet, and bitter all at the same time, and somehow very appropriate for the scene in the movie it's set against (which ends up including an orgy in the desert).
http://www.youtube.com/watch?v=P6_8h64pxTU
This one is also from a late but great guitarist. His name's John Campbell, and he was an absolutely brilliant bluesman worth checking out. Anyways, this one hits most of the right notes for me: the deep bass, sharp high guitar notes come down to smooth low ones, his voice conveys a lot of the pain he talks about, and I love the guitar solo that fades out at the end.
http://www.youtube.com/watch?v=UxXsWrn_u10