I like them a lot more than cheerful songs. I do like more upbeat songs if they are really catchy and have something about them, like those excellent Tamla Motown songs of the 60s. Otherwise its depressing songs for me.

Right now I am listening to 'All My Colours' By Echo & The Bunnymen

What miserable songs do you like?

Misty Blue - Dorothy Moore
http://www.youtube.com/watch?v=uzPxtVimfNM

Heaven Knows I'm Miserable Now by The Smiths.

There's an album called 'The Complete Guide to Insufficiency' by David Thomas Broughton that is brilliantly uncheerful.

Can't beat a bit of Tom Waits.

E.g. this

Bill Withers - Ain't No Sunshine
Manic Street Preachers - Motorcycle Emptiness
Jeff Buckley - Lover you should have come over

Edit: links/found a better song

Mad World - Gary Jules

Bread - Everything I Own
http://www.youtube.com/watch?v=uF-tAUSjXx4

The Moody Blues - Nights In White Satin
http://www.youtube.com/watch?v=WB47ucxQrEQ

Eric Carmen - All By Myself
http://www.youtube.com/watch?v=FXJS1p8lNig

Gilbert O'Sullivan - Alone Again (Naturally)
http://www.youtube.com/watch?v=mv4e9SxPz7E

For melancholy it's got to be Tindersticks for me. Especially their "Curtains" album.

Also, I like some of Bill Callahan's stuff - Jim Cain

Heather Nova's Gloomy Sunday is, well, gloomy.

http://www.youtube.com/watch?v=GRxzkiPc7t8

The Drugs Don't Work - The Verve

This Masquerade- The Carpenters (More melancholy than miserable maybe, although it's pretty bleak.)

Asleep - The Smiths

I think The Smiths are often a very funny band, and oddly would include 'Heavens Knows I'm miserable Now' in that! "I was looking for a job and then I found a job, and heaven knows..." always makes me smile for some reason. Probably just me. but 'Asleep' is beautifully despairing.

Beautiful, but highly miserable, the xx Angels

Like him or loathe him Morrisey is a brilliant lyricist.

cant get much more depressing then this

the shangri la's - remember (walking in the sand)
http://www.youtube.com/watch?v=V5YxtweUxrA

or

lorraine ellison - stay with me baby
http://www.youtube.com/watch?v=6pDBuPK0_DU

Joy Division - Love Will Tear Us Apart
http://www.youtube.com/watch?v=zuuObGsB0No

Sonata Arctica - The Misery
http://www.youtube.com/watch?v=DtY9noiNrXk

John Lennon - Nobody Loves You When You're Down And Out

I used to loathe it but now it's my go-to song when I'm feeling over-dramatic and sorry for myself.

http://www.youtube.com/watch?v=O28PqKx8n2s

The Ballad of Hollis Brown ~ Nina Simone (Dylan cover)
http://www.youtube.com/watch?v=bm-g0p2yTaU

The Smiths - Please Please Please Let Me Get What I Want
http://www.youtube.com/watch?v=yRYpd3_roHg

Cado Belle - September
Blue October - The Worry List
The Gaslight Anthem - National Anthem
Lucinda Williams - Blue
Hurt - World Ain't Right
Lifehouse - Aftermath
Kris Delmhorst - Since You Went Away
Battleme - Dead Man
Hinder - Everybody's Wrong
Madison Violet - The Ransom
Mazzy Star - Fade Into You
Cowboy Junkies - Staring Man

Faith - The Cure

Slow Drowning - The Beloved

Last Exit For The Lost - Fields Of The Nephilim

I would say anything by Joy Division.

Their second album, Closer, is basically Ian Curtis' suicide note.