recommend sad songs

Symphony Number 3 is chilling. I can see myself slowly getting into Classical. Compilations are a good place to start for any genre,but I see what you mean. I have to start somewhere.

yeah compilations are alright to start off with... but really, check out those complete pieces i listed... basic repetoire that is really good... nothing beats going through a COMPLETE piece and not just an excerpt or and individual movement
 
of any era? a couple of 'haunting' pieces that come to mind would be:

Ligeti- Reqieum
Penderecki- Threnody for the Victims of Hiroshima

both are modern pieces and not what most people usually think of when you mention classical... but i would say these are pretty intense and haunting pieces

Yeah these are good ones too, but these create a kind of uncomfortable depressive or sad mood. It depends what you prefer. If you prefer a more traditional classical sound, which creates a more 'beautiful' kind of atmosphere, I would recommend those pieces I mentioned before, namely Rachmaninov's Isle of the Dead, Chopin (any number of pieces work here), Michael Nyman's Piano Concerto (the soundtrack the movie 'The Piano'), as well as Jean Sibelius' 'Swan of Tuonela' and Beethoven's piano sonatas (especially Pathetique and Moonlight sonatas).
 
much doom metal seems to be the answer- katatonia, swallow the sun, and my dying bride have already had the shit recommended out of them

on a less metal note, pink floyd has a number of songs that suit your request. wish you were here is an obvious rec. Porcupine Tree- Mellotron Scratch is another good one

also, ne obliviscaris- forget not
 
a few more that do it for me...

pain of salvation - dedication
pain of salvation - song for the innocent
evergrey - trilogy of the damned
evergrey - as light is our darkness (the song)

these 4 have been spinning alot thorugh my head for the past couple days.