Even Greener Pastures

There is a form of humor or wordplay in English known as "spoonerisms," after a real person, a Reverend William Archibald Spooner, who was famous for doing it accidentally. They don't rhyme. They consists of transposing the beginnings of two words to produce a ludicrous mistake. An example would be "allow me to sew you to a sheet" instead instead of "allow me to show you to a seat."

Thank you for your reply, Allie! Don't worry about your comment being relevant or not, immediately going off topic seems to be almost de rigueur here. And it was very interesting! Would you mind quoting some examples if and when you remember or come across them?

Thank you, Dan! I'd known about Spoonerisms, but hadn't made the connection. I'd thought a Spoonerism was more or less the equivalent of what's called a Kalauer in German, i.e. a rather weak pun/joke/rhyme, as in

"Wie fanden Sie Ihr Schnitzel, mein Herr?" - "Rein zufällig. Unter dem Salatblatt."
"How did you find (= What did you think of) your steak, Sir?" - "Purely by accident. Under the salad leaf."

Das Hotel hat indischen Komfort: das Bad ist jenseits des Ganges.
The hotel has Indian facilities: the bathroom is on the opposite side of the Ganges/hallway.

In Russian, there's a relatively new form of verse. There are only four lines, 9-8-9-2 syllables. Technically it's iamb I suppose. The second and the fourth lines have to rhyme, and the first and the third lines can rhyme too but not necessarily. Usually the last line is a punchline of a joke so to speak (it's usually black humour though). Punctuation marks and capital letters are not allowed. The verses are called "порошки" ("poroshki"). So, for example,

глеб гравитацией томимый
летит пронзая облака
мешает парашют дефектный
слегка

A rough translation into English:

he is by gravitation forced
flies and transfixes cloud lid
obstructed by defective brolly
a bit

© Wasilevsky

I wonder what could be an analogue for this form of verse in English? I think these verses are closer to limericks than Schüttelreime are, aren't they?

Romantic languages have lots of similarities, so I wouldn't be surprised.
My example of poor rhymes can easily be translated to other romantic languages.
The noun ending "ão" in Portuguese is equivalent to the endings "one" (in Italian), "on" (in French) and "ón" (in Spanish).
As for the verbs, my comment about endings and conjugations also apply.
However, I can't speak about the rhyme scheme in those other languages, as I am not aware of them.
But please notice, I said it's easy to make a bad rhyme, I didn't say there weren't good ones!
I am definitely not a poet, but if I had to guess, I'd say in French can possibily be easier than in the other romantic languages because, unlike Spanish, Portuguese and Italian, French is not a phonetic language, just like English, which opens many possibilities. You can rhyme the sounds, not the spelling necessarialy (which in Portuguese would be enough to make a rhyme imperfect) and the way those languages are spoken allow sound combinations (such as the "liasons" in French) that may not occur in other ones. This doensn't mean that those possible rhymes are good, though, as the criteria for what a good rhyme is change from language to language.
I remember I was in class once and, as we were speaking about rhymes, my teacher mentioned the American rapper Eminen. I didn't understand why he was using him as an example, as I had never cared to listen to his songs or mind his work. But, as my teacher insisted that he could come up with good rhymes and I valued his opinion, I decided to give it a look. I read the lyrics of the song "Stan" and thought "what rhymes was he talking about?", as I didn't notice many. Then I decided to listen to the song... "Ah, those!". It was surprising how many sound combinations scaped me as a non native speaker and, even though I can't say I've become one of his members ever since, it was a good experiment. Are those rhymes considered good? I can't tell.
In English, despite the absence of a "rhyme value", there are unusual rhymes and the possibility of using the rythm of the language itself as part of the compostion (as it's a stress-timed  langauge), enriching it, as it's done in limericks, for example. In romantic languages such as Portuguese and Spanish, the sounds are worked in a different way (as they are syllable-timed languages).
So,  how to determine if a rhyme is good or not? It depends!
(This was a gigantic comment and we're not even discussing metric yet!)

Thanks for your comment about Welsh rhyme. My knowledge of Gaeilge is limited to the names of the Luas stations in Dublin, so I can't comment much on that subject, but from what I understod, there may slightly similar things in Portuguese. I mentioned the classification of "value", but there are classifications about phonetics (correspondence of vowels, consonants or both) and also about accentuation (whether the word is accentuad in the last, penultimate or antipenultimate syllable).

If we mention metrics, we'll stay here for years.
If we start about the literary movements of political influence, we'll never finish this discussion!