the Cure - "Bare"
Cocteau Twins - "Golden-Vein "

"The Rainbow Connection", as performed by Willie Nelson.

"Holes" by Mercury Rev is pretty sad.

As is "To Love is to Bury" as performed by the Cowboy Junkies.

"Wicked Game", Chris Isaac.

Many more I can't think of at the moment.

It's Too Late - Carole King
If - Bread, this fucking song has been stuck in my head lately, and making me weep in the privacy of my own home

Superking wrote:
"Holes" by Mercury Rev is pretty sad.

I forgot this one!

Anything Mark Kozelek ever wrote. Start with the RHP album "Down Colorful Hill."

Superking wrote:"The Rainbow Connection", as performed by Willie Nelson.

This makes me cry as well.

I am such a wuss.

Black-"wonderful life"

Orestes - A Perfect Circle
Blissed and Gone - The Smashing Pumpkins
Palimpsest - Smog
Trellisaze - Slowdive (I almost went insane one night listening to this :/)
Your Sickness - Pinback
O I Sleep - Mogwai
The Cold Part - Modest Mouse
Alone In Kyoto - Air
Shibuya - Brian Retzell (Lost In Translation Sndtrk)... or for tha
Wolves, Dead Eyes - Jesu (both off Silver EP)
Celestial (Signal Fills The Void) - Isis
Leif Erikson - Interpol
Wow, this is going off topic and I could probably easily continue with Built to Spill, Death Cab For Cutie, or Black Heart Procession.

I dunno if any of those are in the genre you requested, but hopefully something will appeal to your sensibilities.

maggotbrain- funkadelic

Blame it on My Youth - Chet Baker

Sad Lyrics, Sad tune, Sad trumpet solo.

Sad to the power 3.

Great song.