Another reminder, everybody: unless you’re quoting from a public domain song, please don’t quote more than one verse, or about five lines total.
Including “The Ballad of the Blue Cyclone”, with some memorable characters like the narrator (But I laid in bed three weeks just thinkin’ I believe I coulda took him if I hadn’t been drinkin’!) and his friend Bill (It all happened so quick when that car door slammed, It musta broke something, 'cause the door locks jammed!) and their buddies (who would take on a grizzly with a switch in the woods at night).
Cite for copyright law specifying one verse/5 lines?
Ask Fenris and Eutychus. 
Like father like son
Not flesh nor fish nor bone
A red rag hangs from an open mouth.
Alive at both ends but a little dead in the middle
~Squonk - Genesis
This is SDMB policy, not copyright law.
With regard to song lyrics under copyright we’ve said for a long time that the limit is a verse or five lines.
Ok, no problem; just wanted to be clear.
My example takes more than that to illustrate the characters, so I’ll just post the link:
Song for a Deck Hand’s Daughter by James McMurtry (scroll down to #5).
Actually, that whole album (Too Long in the Wasteland) is loaded with great character descriptions.
There’s something really evocative about the language and descriptions in the Smashing Pumpkin’s Annie Dog - a certain alchemy that I like:
“She is Venus. She is Mars.
She’s electric, and the struggle of.
Upon her face we leave no trace,
but in her stomach, mercury aged.”
“She came from Greece; she had a thirst for knowledge,
She studied sculpture at Saint Martin’s College,
That’s where I caught her eye.
She told me that her Dad was loaded,
I said “In that case I’ll have a rum and coca-cola.”
She said “Fine.””
~ Pulp, Common People
I’ve always considered this to be Zappa’s environmentalist credo.
They Might Be Giants, “Damn Good Times”:
Always makes me think of the girl I was with when I heard this song live.
My first thought was “Suzanne” by Leonard Cohen, but that’s already been mentioned.
“Tangled Up in Blue” has always been one of my favourite Dylan poems/songs because of the intense description of characters, particularly the woman and also her husband “he started dealing in slaves (drugs?) and something inside of him died”… so vivid.
And Taxi especially his description of himself:
Oh, I’ve got something inside me,
To drive a princess blind.
There’s a wild man, wizard,
He’s hiding in me, illuminating my mind.
Tell me you don’t get an idea who that man is, from those four lines alone, never mind the rest of the song.
Why yes, I do love singer/songwriters, how can you tell?
I thought of that song.
But I came here to post this:
And to a lesser extent:
I could probably come up with a lot more great TMBG descriptions. “…His face, which was a paper-white mask of evil…” comes to mind.
Prince, “Little Red Corvette” pretty much all of it but particularly.
Guess I should’ve known
By the way you parked your car sideways
That it wouldn’t last
From Doctor Hook’s “Queen of the Silver Dollar”:
She’s the queen of the Silver Dollar, she rules a smoky kingdom
her scepter is a wineglass, a barstool is her throne.
the jesters flock around her, they fight to win her favors,
to see which one will take the queen of the Silver Dollar home.
From Harry Chapin’s “Shooting Star”:
He was the sun, burning bright and brittle.
She was the moon, shining back his light a little.
He was a shooting star, she was softer and more slowly.
He could not make things possible, but she could make them holy.
I was thinking about posting that one. And I’d like to point out that it was written by Shel Silverstein (as were most of Dr. Hook’s early songs).
George Thorogood’s Luanne:
My oh my, she’s classy;
She’s put together like an Austin Healey chassis
with a tan
He was short and fat and rode out of the West
With a Mogen David on his silver vest
He was mean and nasty right clear through
Which is kind of weird 'cause he was yellow, too
They called him Irving…
-The Ballad of Irving (The 142nd Fastest Gun In The West)
The first two lines of “She Belongs to Me” by Bob Dylan are so perfect that I feel like I know this girl already:
She’s got everything she needs
She’s an artist, she don’t look back.