The op brought this song to mind (which of course, also includes the song it’s parodying)
“[This Song’s] Just Six Words Long” by Weird Al.
Yes, one word – said three times.
As I’ve remarked about this in another recent thread, that’s not really true. The song, which dates back to 1910 (!) actually has four verses. When Herman’s Hermits recorded it in 1965, they ignored all the verses and only sang the chorus. Then they sang the chorus again, saying “Second verse, same as the first!” But calling a chorus a verse doesn’t make it one, any more than calling a tail a leg makes it a leg.
The thing I thought was odd about the song was that, after I learned that Herman’s Hermits basically took an old British Music Hall song and polished it up for modern play, I figured the main change was to speed up the tempo. But it turns out that the original performer, Harry Champion (whose signature song this was) sang it at breakneck speed “his face bathed in sweat and his arms and legs flying in all directions.”. Herman’s Hermits probably sang it slower than old Harry.
The real lyrics to the verses –
I don’t think instrumentals punctuated by a one word shout from the band really qualify as one verse songs. If they did, I could post a list of about fifty surf instrumentals from the Sixties and countless numbers from the Big Band era.
I’m really surprised that I needed to say, “The song as recorded by Herman’s Hermit’s has only one verse.” No, actually, I take that back, I’m not surprised.
Agreed.
The example in the OP goes like this:
Verse (sung once)
Chorus
Repeat chorus
Repeat chorus
The end. So, there’s only one verse, and it’s only sung once. And, yeah, I’m having a hard time thinking of other songs that fit that particular pattern.
Woo hoo, woo hoo hoo. Woo hoo, woo hoo hoo. Woo hoo - woo hoo, woo hoo, woo hoo hoo.
“Eight Line Poem” by David Bowie is, if memory serves, just one verse, no chorus.
You shouldn’t be. Most of our posters are probably a lot younger than that recording.
And you can never tell who knows what. I didn’t realize when I first heard it that it was a much older song that had been dredged out of zombification
Does Tommy’s Holiday Camp by The Who meet the standard?
I thought the Turtles’ “Happy Together” was one verse, but it’s still weird:
Verse 1
Verse 2
Chorus
Verse 3
Chorus
Verse 3
Chorus (Ba ba ba rather than words)
Verse 3
Outro
I’m getting how that’s one verse.
Nor do I understand some of the other submissions like Pink Floyd, “Wish You Were Here” are one verse.
Help a brotha out.
I Want You by the Beatles. Only 17 words long but 7:47.
“Moon in June” by Soft Machine consists of one freeform verse and no chorus. Other than the title, none of its lines rhyme.
This was a trademark of their drummer, Robert Wyatt, who wrote long pieces without any poetic structure and rarely rhymed anything.
I also just stumbled on “Titles” by Barclay James Harvest that was nothing but Beatles lyrics with no chorus.
Depending on the version, “Sea of Love” seems to be either two choruses with one verse in between or one verse and one chorus, both of which get repeated.
Speaking of the Big Band era, it was pretty common early on for the song to be mostly instrumental with the vocalist coming in at the end to belt out a single token verse, so that genre would have plenty of legit examples. IIRC it was Bing Crosby and Sinatra in the late 30’s/early 40’s that were responsible for transitioning into vocal-dominated ensembles (kind of like how hip hop started out all about the DJ, with the MC mostly just ad libbing and hyping the crowd)
Slight Hijack: I shared my homebrew with the band long ago at a free concert. They gave me a CD, all signed it, and Tony wrote “Homebrew!” on it. Was a fan before, and have been since.
They were in Reno on Monday, but it was too hot to go see them (record heat, outdoors, all the smoke from the wildfires), and I didn’t think they would remember me anyway. 
In my experience, three shots of Tequila are quite enough.
@Gatopescado - Wow, cool story. Thanks for sharing. What are some of your favorite songs of theirs? I keep discovering more and more songs I like. They are great songwriters.
I’ve got 2 albums, and like pretty much all of them. When I saw them in the park, they did this one song (off the new album) that I didn’t recognize. It had a long outro with Tony and Miles trading off blistering guitar licks in a ‘call and response’ type of thing. When I was chattin’ and drinkin’ with them, I asked them about it. Miles tells me, “On the album, the second guitar part is played with an Alto Sax”.
I said, gathering all the tact that drinking 4 liters of Homebrew would allow me, “You gotta be fuckin’ kiddin’!” I was thinking to myself, that must be a Train Wreck.
That song was 'Til I Get It Right, and it works. Great tune. Love it!