For complicated reasons I want a sad song-poem (a poem that can be sung if nessacery).
Something sombre, like this: http://ca.youtube.com/watch?v=MQP6CAwnYPw&feature=related, but not cheesy and made by Disney:)
Anyone know of some good laments? Preferably something old.
If you want something old and mournful, can’t beat The Wanderer:
How about Caoineadh Airt Ui Laoghaire/The Lament For Art O’Laoghaire?
http://frontpage.montclair.edu/dennisk/poetry/gael/caoineadh.html
I was thinking of something in English - I couldn’t even pronounce the first one.
How about a little Gilbert O’Sullivan? I swear this guy started the emo thing… This is a great song to sing, especially if you’re Guitar Guy at a party and President Blutarsky isn’t around… 
Amazing Grace?
How sad and mournful do you want? Baptism by Joan Baez is full of them. I’ve always regretted not playing No Man Is An Island from it at my father’s funeral.
There is also Who Knows Where The Time Goes, by Judy Collins.
It’s not old, but you might want to check out “Fire of the Mind” by Coil.
On the Willows from Godspell, from Psalm 137, but w/o the bashing babies heads against the rocks part.
The Beatles’ Eleanor Rigby
As a Smashing Pumpkin afficienado, I’ll donate some helpful mourning songs. Hopefully one will fit the circumstance you’re looking for.
Drug-related mournful song:
This Time
Car Crash related mournful song:
Tear
Just plain Mournful:
Behold! The Nightmare
For Martha sorry for the anime vid, but was the first one I found on youtube search.
Edit: These mostly fit the poem scheme OP was looking for, Billy Corgan did/does consider himself a poet. Spare yourself the trouble of reading his book of poetry book though, utter bleh. 