"I Can Never Go Home Anymore" is probably the biggest downer of all time. It's a beautiful record, but I can't believe such a depressing song became a Top 10 hit! "Leader of the Pack" should count as well - it's said the lead singer of the group was actually in tears while she was recorded the song, and you can hear it in her voice.
Let's not forget:
Bobby Goldsboro - Honey
Simon & Garfunkel - I Am A Rock (maybe not a "sad" song, but its lyrics are very dark and the overall effect is something of a downer even though the song is upbeat)
Petula Clark - Kiss Me Goodbye
The Mamas & The Papas - Monday, Monday
The Skyliners - Since I Don't Have You
Dee Clark - Raindrops
Paul Anka - It's Time to Cry
Dusty Springfield - You Don't Have to Say You Love Me
Brenda Holloway - Every Little Bit Hurts
Poppy Family - Which Way You Goin' Billy? and That's Where I Went Wrong
Brenda Lee - Break It to Me Gently (later excellently covered in 1982 by Juice Newton)
Elvis - In the Ghetto
Walker Bros. - The Sun Ain't Gonna Shine (Anymore)
Going ahead into the '70s, for some reason "Shannon" by Henry Gross always makes me tear up. Perhaps it's because I have a soft spot for dogs.
Others from the '70s:
Janis Ian - At Seventeen
Terry Jacks - Seasons in the Sun
Carpenters - Goodbye to Love and Solitaire
Olivia Newton-John - Please Mr. Please