Duke Ellington: Reminising in Tempo, a haunting tribute to his recently (at the time of composing) departed mother.

Billie Holiday: I'm a Fool to Want You, maybe it's the sad lamenting lyrics or perhaps its the years of drug, physical and emotinal abuse which have cause her voice to crack, but this song is a true tear jerker.

Simon and Garfunkel-Only living boy in new york

Richard Marx - Right here waiting

Sinead O'Connor - nothing compares to you

Stay Together by Seude

No more I love you's Annie Lennox,
or the one that makes me cry everytime, Is meatloafs its all coming back to me.

I'd say it's Gloomy Sunday by Billie Holiday.

Billie Holidays version has a third verse that was never in the Hungarian original, about it being a dream.
There has been a lot of Urban legends spring up around this song, about supposed suicides upon hearing it. The only confirmed suicide I believe is the original Hungarian writer, which I guess is understandable if you listen to the lyrics.

However, it's haunting, but beautiful.
http://www.youtube.com/watch?v=48cTUnUtzx4
_________________
Vidi Vici Veni

I got in touch with my feminine side. She emailed me back saying if I ever contacted her again she'd call the police.

Goombay Dance Band - Seven Tears

Mad World - Gary Jules (or Tears for Fears, an equally good version)

If the topic is sad songs then this one is very drepressing:

Assemblage 23 - Disappoint

Addmittedly, it's not about breaking up with someone you love. Nothing to do with that, but it's sad none the less.

It's a letter to the guy's mother after she committed suicide. Or at least, that's what I think he's singing about.

not very original but
Hurt - Johnny Cash

metalica - one
oasis - stop crying your heart out
counting crows - color blind

Think it's been mentioned before, but as I'm listening to it now Tears in Heaven by Eric Clapton.
_________________
Vidi Vici Veni

I got in touch with my feminine side. She emailed me back saying if I ever contacted her again she'd call the police.