“Stephanie Says,” by Velvet Underground:
Awesomely haunting song! Wish I could find it on karaoke!
A lot of Bright Eyes songs don’t rhyme, or if they do, they’re slant rhymes sprinkled at various points in the songs, not your typical lyrics at all.
Come to think of it, a lot of the songs in Hair don’t rhyme.
Then again, many do, and deliciously:
Am I the only GenXer who is sad to have missed the Sixties? 
The lyrics to Boom Boom by John Lee Hooker don’t rhyme except for the “walk that walk, talk that talk” part.
“White Room” by Jack Bruce and Pete Brown performed by Cream.
FWIW: In Leonard Cohen’s Suzanne the verses about Suzanne do not rhyme. The one about Jesus, and the chorus, do.
They Might Be Giants’ “Minimum Wage”. So as to satisfy the copyright law’s “small excerpt” clause, I’ll only quote half of the lyrics:
*Moonlight in Vermont * by John Blackburn and Karl Suessdorf.
I Got Rhythm by the Brothers Gershwin.
Note to self: know what you’re talking about before posting.
I Got Rhythm has several rhymes in the verse: sunny/money, sigh/buy, song/along, day/way, lot/got. The only rhyme in the chorus is in the bridge, where it rhymes door with more.
Going through my Andrew Lloyd Webber collection, I came up with Jesus Christ Superstar’s “Could We Start Again Please.”
Then I turn on the radio and get the Rolling Stones singing Honky Tonk Woman
To me, Honky Tonk Woman has rhymes. Ride/mind, fight/mind. They are half rhymes, but lots of songs get away with half rhymes for their rhymes.
Just sitting here thinking of it, does Unchained Melody have rhymes?
There are some rhymey parts, but this may only be a partially rhyming song.
For my money, Finger Eleven’s Thousand Mile Wish (<- YouTube) is the best song on that album. I’m pretty sure that it wasn’t more popular because it not only didn’t rhyme, it also didn’t have a chorus.
Tom’s Diner by Suzanne Vega.
If I am recalling all of the lyrics correctly, “Piano Lesson” from The Music Man has no rhymes.
If the factoid from VH1’s Pop-up Video is to be believed, “How Do I Live” by LeAnn Rimes only has one.