Songs with non-rhyming lyrics

Sheryl Crow - All I Wanna Do
The chorus rhymes, but the verses do not.

Leonard Cohen - Suzanne
Some of it rhymes, most of it doesn’t, and the parts that do seem more like coincidence than intentional.

Pearl Jam - Jeremy
If memory serves, nothing in this song rhymes.

Radiohead - Karma Police
There aren’t really that many lyrics in this song as most of them are just repeated. Two of the lines kind of
rhyme ("…girl" → “…ill”), but really only because of the way they are sung.

Suicidal Tendencies - Institutionalized
The pre-chorus and chorus rhyme, but the verses are really just a spoken word story.

Ras Kass - The Nature of the Threat
Some of it rhymes, some of it doesn’t, but that fact that any of it doesn’t rhyme is fairly unique in the hip-hop genre.

Others?

Robbie Robertson - Somewhere Down the Crazy River
It’s another mostly-spoken word story (with one rhyming bit).

Robert Wyatt and Soft Machine stopped writing rhyming lyrics by their second album (I’m not sure about their first). Wyatt continued throughout his songwriting career to write songs without rhyming.

And, of course “Frank Mills” from Hair.

The first one that came to mind when I saw the thread title was ‘Tom’s Diner’ by Suzanne Vega.

Tequila

I don’t feel like going through my music list right now, but a large chunk of the music I listen to does not use end rhyme. Since you mentioned Pearl Jam, I don’t think most of their songs rhyme.

Crazy Ex-Girlfriend has a few: “Let’s Have Intercourse,” “I’m in a Sexy French Depression,” etc…

A whole bunch of early Genesis songs have little to no lyrics that rhyme.

“Tomorrow Never Knows” by the Beatles repeats phrases but otherwise doesn’t rhyme.

The lyrics to “America,” by Simon and Garfulnkel, don’t rhyme.

Nothing Rhymed - Gilbert O’Sullivan

If I give up the seat I’ve been saving
To some elderly lady or man
Am I being a good boy?
Am I your pride and joy?
Mother please if you think say I am

And if while in the course of my duty
I perform an unfortunate take
Would you punish me so
Unbelievably so
Never again will I make that mistake

This feeling inside me could never deny me
The right to be wrong if I choose
And this pleasure I get
From say winning a bet
Is to lose

When I’m drinking my Bonaparte Shandy
Eating more than enough apple pies
Will I glance at my screen
And see real human beings
Starve to death right in front of my eyes

Nothing old, nothing new, nothing ventured
Nothing gained, nothing still-born or lost
Nothing further than proof, nothing wilder than youth
Nothing older than time, nothing sweeter than wine
Nothing physically recklessly, hopelessly blind
Nothing I couldn’t say
Nothing why 'cos today
Nothing rhymed

This feeling inside me could never deny me
The right to be wrong if I choose
And this pleasure I get
From say winning a bet
Is to lose

Nothing good, nothing bad, nothing ventured
Nothing gained, nothing still-born or lost
Nothing further than proof, nothing wilder than youth
Nothing older than time, nothing sweeter than wine
Nothing physically recklessly, hopelessly blind
Nothing I couldn’t say
Nothing why 'cos today
Nothing rhymed

First thing that popped into my head:

This song’s got nothin’ to say
But I’m recording it anyway
I know if I put my mind to it
I know I could find a good rhyme here

Weird Al
This Song Is Just Six Words Long

Boom Boom by John Lee Hooker

Fisher-Z “So Long”

Their intent is clear from the opening couplet:

“When I read your letter I couldn’t believe that you’d gone
I dialed your number but no one answered the phone.”

Amazing successive posts this morning:

Songs with non-rhyming lyrics

Insect stings

There was an Old Man of St. Bees
Who was stung in the arm by a wasp.
When asked, “Does it hurt?”
He replied, “No, it doesn’t,
But I’m so glad it wasn’t a hornet.”

W S Gilbert

Something to Believe In by Poison. There are a few rhymes, but mostly not.

You have a number of songs like Oscar Brand’s A Clean Song, which has two rhyming lines at the very end. You are expecting a rhyme (often an unprintable word) which doesn’t happen.

I was listening to my copy of Best of John Lee Hooker yesterday when I first opened this thread, and thought that a lot of his songs would fit. He does a lot of that half-singing, half-talking thing, and often sounds like he’s ad-libbing the lyrics. One Bourbon One Scotch One Beer is another example.

Benny Ball’s “Shaving Creme” is similar.

“A Hard Rain’s a-Gonna Fall”, Bob Dylan.

(Plenty of Dylan songs, actually, but that’s the first one that came to mind).