I’m sure there’s a technical word for it but I’m not sure what it is. I think it used to be ballad but the meaning has changed somewhat.
Anyway what I mean is a song that basically tells a story.
Like “Ode to Billy Joe,” or “Harper Vally PTA,” or “Wreck of the Edumnd Fitzgerald.”
I don’t know if I have a favourite but I always like the above songs as well as Vicki Lawrences “Night the Lights Went Out in Gerogia.”
You can tell I’m stuck in the 60s and 70s huh? 
I’d have to put “Hurricane” by Bob Dylan at the top of that list, I think.
Pushed closely by Peter Gabriel’s “Biko” and “The Ghosts Of Cable Street” by The Men They Couldn’t Hang.
Hurricane, American Pie or the Argentinian National Anathem
If it counts…Horse With No Name.
I’m partial to John Henry and El Paso. I love the way the dead cowboy accepts his fate. He died for love.
It’s not really a story song (maybe a short story) but I love Gimme Three Steps too.
Some of the sappy stories from the 50’s and 60’s still do it for me – Blind Man in the Bleachers, Patches, Teen Angel, Last Kiss.
Lily, Rosemary and the Jack of Hearts
**Taxi **by Harry Chapin
Have Som Madeira My Dear by The Limeliters
Scenes From An Italian Restaurant by Billy Joel
Alice’s Restaurant. Duh.
Favorite not mentioned so far is The Mariner’s Revenge by The Decemberists. All time favorite is probably American Pie.
“Eurotrash Girl” by Cracker
“Norwegian Wood” by the Beatles
“Spiders and Snakes” by Jim Stafford
Grateful Dead’s “Wharf Rat” has some powerful imagery.
Van Morrisons’ “Madame George” is also very evocative, though Van himself has recently mentioned he’s actually still not sure what his own song is really about…
The Road Goes On Forever by Joe Ely*
“Sonny’s playin’ eight-ball at the joint where Sherry works
When some drunken out-a-towner put his hand up Sherry’s skirt
Sonny took his pool cue–Laid the drunk out on the floor
Stuffed a dollar in her tip jar and walked on out the door
She’s runnin’ right behind him, reachin’ for his hand
The road goes on forever and the party never ends.”
Children’s Story - Slick Rick
Taxi is a good one. Piano Man is right up there.
Widdecombe Fair - traditional English folk song
Barrett’s Privateers by Stan Rogers
Richard Thompson - “1952 Vincent Black Lightning”
I wanna add:
Mama Said by Metallica.
One of the few country songs by the metal band, and about the only song close to country I like.
Good one !
Harry Chapin had a number of them. One of my favourites is “Better Place to Be,” though “Flowers are Red” and “Bummer” are good too.
Elton John’s “Ticking” from the Caribou album is worth mentioning too.
And another from Stan Rogers: “The Mary Ellen Carter.”
You might like another Marty Robbins song called Utah Carroll.
Marty has a bunch of very good story songs.The best story teller in the history of music, IMO.
The Masters Call
Running Gun
The two sequels to El Paso;
El Paso City
Feleena http://www.youtube.com/watch?v=LOPD-p8tM4M
(I really like this video,simple but very neat)
Strawberry Roan
They’re Hanging me Tonight
Big Iron
Billy the Kid
Several others