There is already an interesting thread on songs where the music is cheerful but the lyrics are not.
But ignore the lyrics totally for a minute. Which pop songs have gloomy slow depressing music - songs where if you heard them without lyrics, you’d say “Is this funeral music, or what?”
I’d go first, but I honestly can’t come up with any.
I’ll start with:
“The Freshmen” by Verve Pipe. And the lyrics are no less of a downer.
In the Air Tonight, by Phil Collins? That starts out pretty sparse and bleak-sounding.
The Freshmen is in a minor key, but it’s at a medium-to-medium-fast tempo, and if you hear it without lyrics it sounds thoughtful but energetic. Definitely not “WTF, who died?” kind of music, outside of the very gloomy lyrics.
Would Indian Reservation, especially as sung by Paul Revere and the Raiders, count? Lotsa minor key stuff, and the lyrics, true enough, are a real downer. But it’s definitely a Pop Song
An example (not pop) of what seems like slow depressing music to me, for comparison:
Down In The Park by Tubeway Army (Gary Numan.)
TCMF-2L
Live and Let Die pretty much runs the gamut from maudlin to head-banging to island rhythm.
Indian Reservation’s music is zippy. It gets your toes tapping. Not in a super happy way, but not in a slow depressing way either.
It’s kind of cute how people post the lyrics showing what a downer the song is 
- yeah, I know that part, what I’m trying to find is songs that are depressing without knowing the lyrics.
People have told me I’m crazy for this, but the main riff of “Summer Breeze” always hit me as incredibly gloomy and morose for a song where “everything is alright.”
Hello by Adele
Okay, how about “A Whiter Shade of Pale” by Procol Harum?
I think you found a real one. Thanks!
I wouldn’t call it a depressing song at all, but I agree with you that there’s definitely a weird gloom to the main riff.
I don’t know if you mean Top 40 by “pop music,” but pretty much the entire Mezzanine album by Massive Attack is a gloomy, dark album that just sucks the light right out of the room. A good bit of Portishead would qualify, as well. Joy Division. Depeche Mode.
Well, it does have the organ solo, which gives bonus points for “Whose funeral is this?”
The whole song to me doesn’t end up depressing and slow - the part beginning “…And so it was…” turns brighter and livelier, and the song ends in that mode - but definitely parts of it are slow moving and maybe depressing.
The opening half a minute or so could fit my description, I think. Without the lyrics, is it depressing, or just thoughtful? I’m not sure.
Wicked Game by Chris Isaak and others.
For something perhaps a bit more known, maybe Nirvana’s Something in the Way. I also find NIN’s Hurt to be pretty depressing, even if the lyrics were complete nonsense (but the vocal melody and inflection is still important for conveying the emotion.)
Gets my vote.
Ditto.
“Personal Jesus” was one of the first songs that came to mind when I saw this thread.