There’s also Cows With Guns.
Captain Beaky
reached #5 in the UK charts, 1980.
Deck of Cards, a hit for various people over the years, including Wink Martindale in 1959
Desiderata, Les Crane
Atlantis, Donovan (first part, anyway)
and I was beaten to Big Short Fat Irving.
His cover of Common People was a hit and is actually pretty good: https://www.youtube.com/watch?v=ainyK6fXku0
It’s predominately spoken by Shatner.
Not a hit, but it is by a famous band, and it’s a proper horror story too.
Velvet Underground’s The Gift:
Murray Head never sang a word on his biggest hit One Night in Bangkok.
Willie Nelson is basically doing spoken word at this point. He hasn’t really sung anything for at least a few decades.
She Got the Goldmine, I Got the Shaft
When You’re Hot, You’re Hot
Maybe Blondie - Rapture?
Gregorian Chants? May not be on Billboards Top 100, but they sure have staying power!
Peggy Lee’s recording of “Is That All There Is?” which hit #11 in 1969 has spoken verses alternating with sung choruses.
Oh, well, then, Greta Garbo, and Monroe; Dietrich, and DiMaggio…
Sure, why not? This is kinda fun, as long as I don’t have to listen to them.
But they are sung. I used to be able to read the sheet music and everything. 
Gallant Men by Senator Everett McKinley Dirksen made it to #16 in 1967.
Wild Thing by Senator Bobby (a parody response to Dirksen’s hit) hit #20. The flip side was a version of the song by “Senator Everet McKinley.”
You could argue that Billy Joel does this for long stretches of WE DIDN’T START THE FIRE.
To me, some sound sung, sure. Others sound like a chant. Maybe it depends on how they’re performed.
Wyatt Earp Makes Me Burp-- Spike Jones