Depressing is such a harsh term. It also differs from person to person as we all absorb music in our own ways. Is Joy Division depressing? I wouldn't say so. Sad and depressing are such different things. I mean, very often the mood a song stirs up depend on our personal memories attached to it.
I rather avoid to call songs depressing because very often the sad songs make me somehow feel better and less alone when I feel sad. So let's list some songs which I would label as sad songs (but without negative undertone)
The God Machine - It's all over
Sophia - (Death comes) so slow
Evanescence - My immortal
Echo & The Bunnymen - Ocean rain (my favourite song all-time, but a sad one lyrically)
Manic Street Preachers - William's last words
On a totally different level, check out Salem's (another Israeli metal band) song "Ha´Ayara Bo'Eret", a doom metal version of an old 1938 poem by Mordechai Gebirtig which was a warning for the holocaust (initially written in Yiddish language and named "S'brennt"). Salem's metal cover in Hebrew is very haunting, and the video (using real footage from the war - so not for sensitive eyes) is simply horrifying. It is a fantastic anti-war statement and a message to never forget what happened...
at the same time you can consider it a very sad song because, looking at current ongoings in Europe, people haven't learnt from their past and stigmatisation based on ethnicity and religion are ongoing. That to me may be sadder than any song that deals with themes such as suicide or personal grief.
WARNING: those with sensible eyes better not watch the video. It was intended as anti-war statement, not to shock, nonetheless it can come across as shocking to some. If you are easily moved by such images, better just check the audio of that song.