Oh, come on, people! Let’s up the cheesiness quotient a bit, shall we?
Knock Three Times
Copacabana
Heh–once Joe Ely’s performed a song, it becomes “his”–no matter who actually wrote it. He did a pretty good job on his own Me & Billy the Kid. Here we see the Flatlanders back Tom Russell in Joe’s Indian Cowboy.
Which Townes van Zandt used to play, along with his own story songs like “Tecumseh Valley” & “The Ballad of Poncho & Lefty.”
There are lots of folkie stories sung down here–but I sang along many times to Stan Rogers’ “Barrett’s Privateers” as sung by Bill Staines, a visiting New Englander. And was amazed when Paul Gross used it in Due South…
Edited to add: No, I can’t pick just one.
Came in to post that one. Also my favorite thanksgiving song.
Much as I love Marty Robbins, the best storyteller in the history of music is Tom T. Hall. In addition to writing Harper Valley P.T.A., he also wrote gems like God Came Through Belleville, Georgia, I Remember the Day that Clayton Delaney Died and, of course, Old Dogs, Children and Watermelon Wine.
He also wrote tons of crap, but at his best, there was no one who could tell a story in 2 1/2 minutes like Tom T. Hall.
Hows about some more Arlo Guthrie?
City of New Orleans
Coming into Los Angeles
The REAL “City of New Orleans” was by Steve Goodman, though I believe his “passing towns that have no names” was improved by Arlo’s “passing trains that have no names.”
“The Wreck of the Edmund Fitzgerald” is special, to me, because I knew a guy who sailed on that run. They supposedly stopped in either Cleveland, Gary or Chicago (I don’t recall), he got drunk and into a fight (the two went together for him), and missed the boat when it sailed the next morning.
One of my very best friends lives(or lived) right next door to the captain of the SS Arthur M. Anderson,the ship that was trailing the EF when it went down.
Lets have some fun with Patricia the Stripper by Chris De Burgh.
Also by de Burgh - Crusader, Spanish Train, and Just Another Poor Boy.
Agreed. A train without a name was a freight train. A train that had a name was a passenger train: the City of New Orleans, the Twentieth Century Limited, the California Zephyr–all well-known passenger trains. For train buffs, Arlo’s change conjured up a mind’s-eye vision familiar to any train traveller of passing freights on sidings. A “town without a name” just doesn’t work as well, IMHO.
And good call, kunilou, on Tom T. Hall. I came in here to mention “Old Dogs, Children, and Watermelon Wine,” but you beat me to it.
Tom Waits - Romeo is Bleeding, or Frank’s Wild Years, or Murder in the Red Barn
Now the ravens nest in the rotted roof
of Chenoweth’s old place
and no one’s asking Cal
about that scar upon his face
'Cause there’s nothing strange
about an axe with bloodstains in the barn
There’s always some killing
you’ve got to do around the farm
Seriously, it’s been my favorite “story” song since I was a kid. I used to hear it once a year (on New Year’s Eve… Midnight Special or something like that? On NPR), and even before I had a clue what it meant, it was the song I always looked forward to.
Of course, 'round about 9 or so, I figured out what it was about, and I shocked myself!
By high school, my girlfriends and I were singing it at the Ren Faire. No, we didn’t officially work there, we’d just start singing it in three part harmony. Made some fine tips, too!
I would suggest these two as the best “story songs”:
“Devil Went Down to Georgia” by Charlie Daniels
“Boy Named Sue” by Johnny Cash
I thought I was gonna get to be the first one to mention this! Missed it by that much! Yes, I love this song.
Also, speaking of Harry Chapin, “Cat’s in the Cradle.”
Billy Joel, “Scenes from an Italian Restaurant”
Sting, “The Soul Cages” <– a very underrated song; I adore it.
Jonathan Coulton, “Skullcrusher Mountain,” “Code Monkey,” “Creepy Doll,” “The Future Soon” … rather a lot, actually.
Jeff, I gotta find that one – I love murder ballards. Long Black Veil is a favorite.
I can came in here to mention that. Marvelously creepy revenge song.
On a similar note, Flight of the Conchord’s “Petrov, Yelyena and Me.” Marvelously hilarious cannibalism. 
Ooh! Mentioning Flight of the Conchords reminds me of the Main Street Singers’ “Potato’s in the Paddy Wagon” and Mitch & Mickey’s “The Story of Bobby and June.”
Dixie Chicken Little Feat
No fair! I was going to say Gabriel’s Biko and…
The Colours by TMTCH.
I love the line “While Pitt stood helpless we were waiting for Bonaparte”
“Pleasures of the Harbor”, or “The Highwayman”, both by Phil Ochs.