My primary school once did a "Christmas sing-along", with parents invited, and the head teacher pointing at the words on a flip chart with a long stick, all neatly handwritten. (1980s technology, no Powerpoints there!) One song was "She'll be coming 'round the mountain". When it got to the verse "she'll be wearing pink pyjamas", one of the dinner ladies appeared in a pink tracksuit, and was chased by the Head with her stick.
"Here sits a monkey on a chair, chair, chair, she lost all her true loves" (which we children said as "chew loves"), in which people took turns to do some sort of action, but you had to choose one which nobody else had done.
"Can you mend a chair?" said the crow to the frog.
"I can do that," said the nosey dog.
(Actions of mending a chair)
Last verse: "Can you run away?" said the crow to the frog.
The Big Ship Sails on the Ally Ally Oh, with its complicated movements: everyone held hands in a line, and the head of the line would walk through the first "arch" formed by the last two people, and this was repeated, so that everyone ended up with arms crossed.
"Sally go round the sun, Sally go round the moon, Sally go round the chimney pots on a Sunday afternoon." The catch was that the next verse would be Monday, Tuesday, etc. Any child who sang the wrong day was out.
The Muffin Man. Two of us were blindfolded, and everyone would sing "You can't see the Muffin Man, the Muffin Man" etc. One person pointed at by the teacher would then sing in a disguised voice: "I can see the Muffin Man", and the two who couldn't see would guess who it was.
We had a record of Pete Seeger visits Sesame Street, which had songs such as:
Skip to my Lou.
This land is your land.
The garbage song. "What will we do when there's nothing left to watch, nothing left to touch, nothing left to walk upon, nothing left to talk upon, nothing left to see, but garbage".