Songs without rhyme....

[Diamond Dog]

The night was clear
and the moon was yellow
And the leaves
came
tumbling
down

Followed by :

I was standing on the corner
When I heard my bulldog bark
He was barkin' at the two men who were gamblin'
In the dark
It was Stagger Lee and Billy
Two men who gambled late
Stagger Lee threw seven
Billy swore that he threw eight
Stagger Lee told Billy
I can't let you go with that
You have won all my money and my brand new
Stetson hat...


So, no, not really

[Rayge]

I was standing on the corner
When I heard my bulldog bark

I always heard that as 'fool dog', which makes more sense.

[Stalky the Paranoid Pooch]

I always heard that as 'fool dog', which makes more sense.

Oy!

[Your Friendly Neighbourhood Postman]

Songs without reason.

I'd buy that mixtape.

Surely the next U2 album.

[Robert]

Of the examples given, especially the one by the old man, there is quite a lot of inner rhyme. That usually works pretty well in songs. Better often than in poems.
Watch the use of ‘o’ and ‘oo’ in Ray’s example.

The ‘o’ and ‘oo’ can also be seen in Fantastic Voyage quoted above.

[Quaco]

Positively 4th Street

It may seem like it, like each line stands on its own, but it rhymes consistently all through it.

[pig bodine]

The Ballad Of Jerry Curlan