First one I thought of too. Second one:
“I must admit I felt a little uneasy
When she bent down to tie the laces of my shoe
Tangled up in blue”
Nick Cave has some interesting rhymes. In The Curse of Millhaven he rhymes a-roaming, a-combing, moaning, a-flowing, going, phoning, foaming, a-going, stowing, blowing, and finally, a home in. Then the very last verse he doesn’t bother and chucks groovy in there.
In *O’Malley’s Bar" he has these gems:
Well, you know those fish with the swollen lips
That clean the ocean floor
When I looked at poor O’Malley’s wife
That’s exactly what I saw
I jammed the barrel under her chin
And her face looked raw and vicious
Her head it landed in the sink
With all the dirty dishes
I’ve lived in this town for thirty years
And to no-one I am a stranger
And I put new bullets in my gun
Chamber upon chamber
I shot Richard Holmes in the stomach
And gingerly he sat down
And he whispered weirdly, “No offense”
And then lay upon the ground
“None taken”, I replied to him
To which he gave a little cough
With blazing wings I neatly aimed
And blew his head completely off
Thanks for the double TIL on that. Can’t believe I’d never heard of jump blues before.
There’s 10CC going for an omitted rhyme in “The Worst Band in the World”:
It’s one thing to know it but another to admit
We’re the worst band in the world
But we don’t give a
I’ll spare linking.
I think technically that’s assonance, not rhyming, but I personally usually give a pass on that.
I’m stunned nobody has quoted “Rock of Gibraltar” yet. Nick rhymes the landmark with “falter” and “alter” but also drops in this gem:
Under the big yellow moon
On our honeymoon
I took you on a trip to Malta
And all through the night
You held me so tight
Your great, steady Rock of Gibraltar
It’s a bit more than just plain assonance, as you also have the same schwa-l at the end there, so you also have consonance. You could put it under the broad category of slant or imperfect rhyme, or near rhyme, or whatever you want to call it. I think – and maybe I’m wrong – that @WOOKINPANUBv.2 was also commenting on the “cats in the cradle” imagery.
Tom Lehrer is great at deliberately making far-fetched rhymes/puns.
And Nick Cave is superb. Also, Alex Turner.
Yup. Based on others’ responses I thought we were including lyrics that are put together to “kind of” rhyme. It’s all good. Plus, I learned the words “assonance” and “consonance” 
Yeah, assonance is repetition of vowel sounds; alliteration of initial sounds (usually consonant sounds); consonance is of consonant sounds anywhere in the word. Then you have masculine rhymes, which end only a terminal stressed syllable (“mate” and “great,” “correct” and “infect.”) and feminine rhymes, in which rhyming unstressed syllables follow the rhymed stressed syllable (“syllable” and “billable,” for example.) Identity rhyme (rhyming a word with itself or a word that sounds like itself, e.g. “rhyme” and “rime,” or in the stressed parts of two different words like “cruise” and “accrues.” Rime riche is a similar concept.) Identity rhymes, for whatever reason, are often viewed as “lazy” or not rhymes in English prosody, but they occur in other languages commonly (like French.) I personally have no issue with them (as given in my Black Sabbath example above.) More colors to work with in the palette.
A lot of more contemporary poetry (and by “contemporary” I’m talking the last hundred years) when opting for traditional forms often choose these “softer” types of rhymes, often mixing them with perfect rhymes.
For example, take Seamus Heaney’s first eight lines of Glanmore Sonnet V, in ABAB CDCD rhyme structure:
Soft corrugations in the boortree’s trunk,
Its green young shoots, its rods like freckled solder:
It was our bower as children, a greenish, dank
And snapping memory as I get older.
And elderberry I have learned to call it.
I love its blooms like saucers brimmed with meal,
Its berries a swart caviar of shot,
A buoyant spawn, a light bruised out of purple.
We have these rhymes: “trunk/dank,” “solder/older,” “it/shot,” “meal/purple.” And his final couplet, rhymes “crouch” with “hush.”
I’ve always enjoyed the sound of these subtler “rhymes.” (He does have a perfect rhyme with “wine/mine” in the third quatrain, but that’s the only traditional rhyme (depending on how “solder” and “older” are pronounced) in this particular sonnet. In the other ones in this sonnet cycle, he does use more perfect rhymes, but interspersed with many slant rhymes.
From ELP’s “Still You Turn Me On” comes this bit of deathless rhyme:
“… Every day a little sadder
A little madder
Someone get me a ladder.”
Yeah, but Steve Taylor wrote satirical stuff. I’m sure he intended for that rhyme to be bad.
It’s a song I like from a period when Neil Diamond was great, but
“I am,” I said
To no one there
An no one heard at all
Not even the chair
is crap.
And the two opening verses, before that, have several rhymes that aren’t exactly the stuff of strenuous mental gymnastics.
Maybe it’s just me, but in I Need you to Turn to, Elton John sings,
“You’re not a ship to carry my life
You are nailed to my love in many lonely nights
I’ve strayed from the cottages and found myself here
For I need your love, your love protects my fears.”
He also rhymes “control” with “cold.”
From Joseph and the Amazing Technicolor Dreamcoat:
“Greatest man since Noah,
Only goes to show-ah…”
Quality of the rhyme aside, did no one point out to Tim Rice what “show-ah” sounds like?
Considering that he wrote a deliberately bad rap song called “Bad Rap”, you may have a point.
I assume he must have known.
If grammar tortured to make a rhyme counts, then “America” from “West Side Story” must be a contender, for this bit:
I like the island Manhattan,
Smoke on your pipe,
And put that in
Dave Barry got four columns and a book out of this “rhyme” as it kicked off his Bad Songs Survey back in the 90s. Dave Barry's Book of Bad Songs - Wikipedia The other Neil Diamond lyric from which he got mileage was “Song she sang to me/Song she brang to me.” (“Of course, I think those lyrics are brilliant, but they brang out a lot of hostility in my readers.”)
I love that book. If you’re of the right age, or have knowledge of the songs of that period, it is pants-pissingly hilarious.
Perhaps I should clarify that I like this Neil Diamond song and others from that time because my mother played them often (well, mothers, you know…) and the music is good, but I did not speak English at the time, so the lyrics went right over me.