Tom Jones “I’ll Never Fall in Love Again”
Tom Jones “Delilah”
Two more that I haven’t seen mentioned yet, as sung by Red Sovine: Tear-jerker trucker songs Phantom 309 and Ballad of Teddy Bear:
“Teddy Bear” had two follow-up sequels, one by Red Sovine. In one, Teddy Bear gets the medical treatment he needs and recovers. In the other, he gets steadily sicker and dies.
Here’s a song that’s guaranteed to bring a tear to your eye: Ballad of a Dog Named Stains by Red Peters.
My high school band teacher said that a ballad is a song in which the lyrics tell a story. As for the music:words ratio or having a chorus, that varies. Not sure if this fits but it’s a fave.
I got the impression that @elfkin477 was looking for songs where the storytelling part was spoken, not sung. Am I wrong? Many of the examples that have been offered don’t fit that criterion.
Boney M “Rasputin”
Boney M “Ma Baker”
A lot of the tracks mentioned here, I think, fall into the “kinda-sorta” group.
How exactly does a song have to fit OP’s rules? The two that I just posted, Phantom 309 and Ballad of Teddy Bear, are spoken, but don’t have any sung chorus. Does that work?
Dark Lady - Cher
Maybe more like Lou Reed?
There’s “spoken,” and then there’s “spoken”:
Lorne Greene “Ringo”
William Shatner “Rocket Man”
Ghost riders in the sky:
There are several versions. I like Johnny Cash’s. It’s not a complex story, but a great song.
A few I don’t think have been mentioned yet:
Jimmy Dean – Big Bad John
Bob Dylan – Hurricane
Michael Martin Murphey – Wildfire
Dolly Parton – Me and Little Andy
Dolly Parton – Coat of Many Colors
Teen Angel, Where Oh Where Can My Baby Be, Dead Man’s Curve…OH!
Bloodrock – D.O.A.
The sensational Alex Harvey Band talk/sing about the Boston tea party…
Coven - One Tin Soldier
I love this shit. 
I thought about “Teddy Bear” (one of the first 45s I ever bought), but it has no chorus (as the OP described), and really no singing at all – just Sovine talking over a music bed.
I was shocked it hadn’t been put up already. Everybody knows that song, don’t they?
One of the best songs on one of his best album, for sure!
I was thrilled when Zeke came along and even happier the first time I heard this:
I found out about this one from the Dope!
God’s Own Drunk, by Jimmy Buffet.