This was so hard. I think there is probably a counter argument that every song is about sex, directly or indirectly. Inspired by @dave and requested by @Z.
  1. "Ben" by Michael Jackson
    A song about being friends with a rat.
  2. "Pollo Asado" by Ween
    A song about ordering Mexican food.
  3. "Chicken In Black" by Johnny Cash
    A song about a brain transplant between Cash, a dead bank robber, and a chicken. The chicken ends up with Cash's brain, and goes on tour singing his songs.
  4. "I Would Die 4 U" by Prince
    A song about being Jesus.
  5. "Inní mér syngur vitleysingur" by Sigur Rós
    A song about asexual Icelandic elves frolicking in the woods.
  6. "Making Plans For Nigel" by XTC
    A song about overbearing parents and Britain's slide into Thatcherism.
  7. "Outdoor Miner" by Wire
    A song about the short life of an insect.
  8. "Werewolves of London" by Warren Zevon
    A song about British werewolves and Chinese food.
  9. "Istanbul (Not Constantinople)" by The Four Lads, notably covered by They Might Be Giants
    A song about formally renaming Constantinople to Istanbul in 1930.
  10. "Fish Heads" by Barnes & Barnes
    A song about fish heads. With a music video directed by and starring a young Bill Paxton.
  11. "Spoonman" by Soundgarden
    A song about a street musician who plays the spoons. It is not about spooning. Get your minds out of the gutter.
  12. Heroin - the Velvet Underground (it's about heroin)
    Suggested by @ariannastern
  13. Rock Lobster - B52s
    Suggested by @originalamericantrt
  14. A change gonna come - Sam cooke
    About the civil rights movement
    Suggested by @gilbaron
  15. Dark side of the moon - pink Floyd
    About syd Barrett going mad
    Suggested by @gilbaron
  16. Yellow submarine - beatles
    Oh to go, no one knows what this song is about, not even him but clearly not sex
    Suggested by @gilbaron
  17. Strange fruit - Billie hokiday
    Civil rights pt 2
    Suggested by @gilbaron
  18. Sliver - nirvana
    About going to grandmas hiuse
    Suggested by @gilbaron
  19. Leper messiah - metallica
    Suggested by @gilbaron
  20. Rhyme of the ancient mariner - iron maiden
    Suggested by @gilbaron
  21. 905 by The Who
    About a guy who has been created in a laboratory petri-dish. Yes, the song refers to his "manhood" and puberty, but it's the most unsexy song possible. However, it fucking ROCKS and you should listen to it right now.
    Suggested by @evan
  22. Angel
    Sarah machlachlan
    Suggested by @dave
  23. Hunter by Bjork
    About her leaving Iceland to be great and conquer the world.
    Suggested by @olive
  24. Brave by Sara Bareilles
    I played this game with an 8-year old who complained that every song was about "love". It's SO HARD to prove him wrong.
    Suggested by @shinyunicorn