What a great topic! Music is my biggest comfort when I'm feeling bad. And listening to sad songs can help get the tears out when I'm otherwise unable to.

I couldn't begin to list specific songs - there are too many - but here are some albums I've turned to, at one time or another.

The Cure - Distintigration
The Cure - Faith
Cranes - Wings of Joy
Bjork - Selmasongs
Bjork - Vespertine
Sinead O'Connor - I Do Not Want What I Haven't Got
Sinead O'Connor - Gospel Oak EP
Concrete Blonde - Bloodletting
The Sundays - Reading, Writing and Arithmetic
Joni Mitchell - Blue
Kate Bush - Aerial
Nico - Chelsea Girl

Just off the top of my head. I'm sure there's more.
And of course, many individual songs, the most recent and strangest (for me) is Daniel, by Elton John.