I listen to pretty much only sad music. So the songs I have are grievous ones! But here goes:
Emmylou Harris: Goodbye
Jann Arden: Cherry Popsicle
Tori Amos: Hey Jupiter, 1000 Oceans
Kate Bush: You're the One (holy ****! the lyrics are cheesy, but I bawl every time I hear this one!)
Indigo Girls: Ghost
Sinead O'Connor: Nothing Compares 2 U, What Does Not Belong To Me
Loreena McKennitt: Dante's Prayer (another WEEPER!!!)
Lucinda Williams: Lonely Girls, I Envy The Wind
Tanita Tikara: Lovers in the City, I Might be Crying (brace yourself for these ones too!)
Joni Mitchell: A Case of You
I'm a believer in wallowing in self pity!

So, if you wish to follow my lead, listen to these ones!