Ever since I was a little kid VAUGHN MONROE, GHOST RIDERS IN THE SKY, A COWBOY LEGEND has been the Gold Standard for such things for me.
If that’s not your basis for comparison, what is? 
Convoy? It’s the first thing that popped into my head, but please note that I hate hate HATE it.
Good example, in any case. Marty Robbins “El Paso” is another contender for me.
It’s high on my list as well.
The Devil Went Down To Georgia or Uneasy Rider, both by the Charlie Daniels Band.
The Ballad of Irving the 144th Fastest Gun in the West
Cold Missouri Waters https://youtu.be/KgQNeGPJdcQ
Thanks for that! Makes the thread worth it. New to me.
Squeeze, “up the junction” or perhaps “labelled with love”
Alice’s Restaurant.
“Lily, Rosemary and the Jack of Hearts” - Bob Dylan
“Pancho and Lefty” - by either Willie Nelson and Merle Haggard or Townes Van Zandt(who wrote and originally recorded it)
how about Harry Chapin ?
Almost all his songs tell a story, and with emotion.
Taxi and its sequel are probably his best.
Excellent choices. The Dylan is new to me, too.
Your mention reminds me (for some reason I can’t name) of Al Stewart - Roads To Moscow as well as some other things of his.
Would a Boy Named Sue qualify?
I some way, for sure. There’s a line between story songs and novelty songs but I’m not sure where to draw it. Some Country songs are in that area, for my tastes.
Others I can name offhand:
Sixteen Tons
Davy Crockett
Tennessee Stud
And here’s another Vaughn Monroe oldie that’s probably in that same box: Vaughn Monroe - Black Denim Trousers and Motorcycle Boots
which may have prompted Robert Mitchum to write and produce the movie: Robert Mitchum sings The Ballad of Thunder Road
American Pie
Highwayman by Lorena McKennett
Sam Stone John Prine
is House Of The Rising Sun a story? If so, my favorite version is by Bob Dylan (not available on YouTube).
The whole album is good, I rate every track at least a 7 out of 10, several 9/10. Blood On The Tracks. I rate Idiot Wind 10/10 but I guess people will disagree what is the best song on that album… so many good choices.