Can’t believe I forgot The Legend of John Henry’s Hammer - that might just be my #1.
Her First Mistake by Lyle Lovett
This one’s been mentioned a few times. George’s version is a way better story, but let’s give credit where it’s due- it’s John Lee Hooker’s song. My favourite story song by John Lee is Boogie Chillun.
Lots of greats in this thread. The latest one I’ve been loving is Van Lear Rose by Loretta Lynn.
Heaps of Paul Kelly songs - Who’s Gonna Make the Gravy, To Her Door, From Little Things Big Things Grow,** Bradman**
and of course Tribute by Tenacious D
Now that I’ve got out the old vinyl and had a fresh look at it, I have to correct and elaborate on this a bit 'cause the single’s just so cute. The vinyl single’s back side has the lyrics printed in the format of an actual play in three acts, complete with a cast of characters and scene description. The front side of the sleeve (with set design credited to XTC frontman Andy Partridge) has a gatefold of a rather Victorian-looking theater proscenium with a large cutout in the center, showing the drawing on the single’s sleeve of a crosssection of Graham’s house (kitchen downstairs, Graham’s bedroom upstairs). The insert of the song’s characters (Graham, his [literally portrayed] wasp-headed mother, his stodgy father, the cop, and the judge) has the figures standing on long rectangular strips that you’re encouraged to cut out and use as hidden puppet-poles, sliding them back and forth in front of their “stage,” in what would surely rank as one of the dorkiest indulgences of music fan geekery ever. And no, I have not and will not play with the stage puppets; that would ruin the value of my precious collectible! :wally
This fan site link has it all: seven pics of the single and the artwork; the band’s comments about the recording of the song, lyrics, lyrics as printed out in play form, discography notes…
City of New Orleans Arlo Guthery
Vincent Don McLean
- Cats in the Cradle* Harry Chapin
Turn the Page Bob Seger
(Ticky, Tacky) Little Boxes (All in a Row) by Pete Seeger
The Flying Saucer by Buchanan & Goodman
My older brother turned me on to Harry Nilsson ages ago. I’ll date myself by saying this-when The Point was a new album, one of the Phila TV stations did a simulcast-you listened to the audio on your stereo. I have the album on vinyl, and also the VHS tape. Heck, I remember the Chrysler commercials for the Dodge Arrow that used Harry’s music. 
I like Eric Bogle’s version, because it’s just him and his instrument. Very folksy and personal. It feels like you’re there in the room, listening to him tell the story.
Nobody does story songs like Steve Earle! There’s “Copperhead Road,” “Johnny Come Lately,” “Tom Ames’ Prayer,” “Taneytown,” etc.
My number one Steve Earle story song, I guess, is Billy Austin, because the message is so damned powerful.
Another master of the story song was Steve Earle’s mentor, Townes Van Zandt. My favorite of his would probably be Pancho and Lefty.
Cats in the Cradle (took 66 posts to mention this!)
Fred Jones pt.2 by Ben Folds Five is an excellent one too.
Miss Otis Regrets
Stagger Lee
The Gift - Velvet Underground
Call of the West - Wall of Voodoo
Sniper (Am I?) Harry Chapin
Ode to Billie Joe Bobbi gentry
“Band on the Run” - Paul McCartney & Wings
“Year of the Cat” - Al Stewart
The Devil Went Down to Georgia has been mentioned, but no one has mentioned Uneasy Rider yet?
Also, I’ll throw in The Mary Ellen Carter by Stan Fogarty as a companion to Edmund Fitzgerald.
Also One Week by the Barenaked Ladies.
In a slightly different vein, Calypso Blues, preferably as done by Harry Belefonte or Nat King Cole.
Next?
Rose Tattoo is THE shit!
My two faves (Butcher & Fast Eddy aside):
Rat Trap by The Boomtown Rats
Down in the Tube Station at Midnight by The Jam
Not terribly storyish, but I prefer pithier fare.
Many of my favorites are listed here. One that nobody has mentioned yet: My Sister by Tindersticks. The story of a life that starts at the bottom and it’s downhill all the way from there. It’s very depressing.
I can’t believe I forgot He Stopped Loving Her Today by George Jones. That’s been a favorite of mine for many years.
Agreed on Tribute by the D. I haven’t listened to that in awhile, I’ll have to dig it out now :D.
Vincent, Don McLean
Lola, The Kinks
And many of the others previously listed.