When my mother was a child, in Oklahoma, they sang this to the tune of The Old Grey Mare, and instead of “That’s what we eat at school,” it said “Swimming in Grandma’s stew,” which also formed the refreain.
We used to sing “my country tis of thee…”… um, does that count? 
It rolled through the garden,
and under a bush,
When I found my poor meatball
it was nothing but mush.
Speaking of Girl Scouts, I learned this one from a scouting friend and still love it:
Black socks, they never get dirty
the longer you wear them the stronger they get.
Some-times, I think I should wash them
but something inside me says ‘no, no, not yet!’
…it can be sung as a round.
But early next summer,
it grew into a tree,
which grew lovely meatballs
all covered with cheese.
Excellent! 
I’m adding that to my repertoire.
This one reminds me of a round we used to sing:
There was an old woman from Clyde
who ate too many apples and died.
The apples fermented
inside the lamented
Formed cider inside her insides
And when I was little I made up this nonsensical little verse to the tune of Beethoven’s Ode to Joy:
In this world of wild wide women
Why were we what we were?
Windowpanes and wild wide women
Were why we were what we were
It’s to the tune of the Marine Corps Hymn.
From the halls of Montezuma
To the shores of Tripoli . . .
I think the variations of this tune are interesting. I wonder if they’re regional in nature. Our version went like this:
Great green gobs of greasy grimy gopher guts
Mutilated monkey meat, little birdies’ bloody feet
French fried eyeballs, leftover fingernails
And I forgot my spoon. (but I have a straw)
I was a Girl Scout before I was born (my mom was a Girl Scout leader) so I know all the great songs!
How bout:
The classic sung to Arkansas Traveller
I’m bringing home a baby bumblebee
Won’t my mommy be so proud of me
I’m bringing home a baby bumblebee
(spoken) Ouch! It stung me!
I’m squishing up my baby bumblebee
Won’t my mommy be so proud of me
I’m squishing up my baby bumblebee
Eww! what a mess
I’m licking up my baby bumblebee
Won’t my mommy be so proud of me
I’m squishing up my baby bumblebee
Ohh! I feel sick!
I’m throwing up my baby bumblebee
Won’t my mommy be so proud of me
I’m throwing up my baby bumblebee
Ewww! Another mess!
I’m sweeping up my baby bumblebee
Won’t my mommy be so proud of me,
I’m sweeping up my baby bumblebee…
Hi mom!
The version of the worm song I know:
Nobody likes me, everybody hates me
I think I’ll go eat worms
Big fat juicy ones, little bitty squirmy ones
Watch how they wiggle and squirm
First you bite the heads off, then you suck the juice up
then you throw the skins away
(unless you like them)
Nobody knows how I eat worms
Three times a day
And lastly, (but I’ve got more!) I’ll share my very favorite silly Girl Scout song
The Billboard Song
As I was walking down the street one dark and dreary day
I came upon a billboard, and much to my dismay
The sign was torn and tattered from the storm the night before
The wind and rain had done its job and this is what I saw:
Smoke Coca-Cola cigarettes, chew Wrigley Spearmint beer
Ken-L-Ration dog food makes your complexion clear
Simonize your baby in a Hershey’s candy bar
And Texaco’s the beauty cream that’s used by all the stars
Sooooo
Take your next vacation in a brand-new Frigidaire
Learn to play the piano in your winter underwear
Doctors say that babies should smoke until they’re three
And people over 65 should bathe in Lipton Tea
With Flow-Thru Teabags.
The funny thing is that the songs didn’t stop when we got older.
One of the silly ones from college had the last verse:
My father peddles opium
My mother’s on the dole;
My sister was a prostitute but now she’s on parole;
My brother owns a restaurant with bedrooms in the rear,
But none of them will talk to me 'cuz I’m an engineer.
I always sang that one to the tune of the drunken Scotsman song.
Caj
[You know, the one drunken Scotsman song. Ever written.]
My cousin and I used to singa different version…
On top of spaghetti
All covered with blood
I shot my poor teacher
With a .44 stud.
I went to her funeral
I went to her grave
Everybody threw flowers,
I threw a grenade.
I looked in the paper
She wasn’t quite dead
So I went to her coffin
And blew off her head.
There were a lot more verses, half of them made up on the spot, btu yeah. Dunno where that one came from, but we wrote a lot of songs like that. I think our parents were kinda concerned for a while.
We sang it thus:
On top of Old Smokey
All covered with blood
I shot my poor teacher
With a 44 slug.
I went to her funeral
I went to her grave
Some people threw flowers,
I threw a grenade.
I watched her go up, up, up,
I watched her go down,
I watched her go sphbllt,
All over the ground.
I wondered if someone would come up with the “meatball” song. I learned it from this horrible american kid who turned up in Belfast in about 1967. He seemed to be obsessed with dog-droppings.
“The Drunken Scotsman” song has to be “I belong to Glasgow”.
I loved the black socks one! 
I did a search on those lyrics just now, to see if there were more verses (there are) and found this:
http://www.yorku.ca/earmstro/speech/dialects/cockney/blacksocks_cockney.pdf
I’m currently sitting here LMAO but you might need to have taken a phonetics class to get the humour… but I think the main reason I am laughing is because someone felt the need to study, document and publish the findings…
You folks have such great gross songs. The only song I can remember is the one sung to The Stars and Stripes Forever.
Be kind to your web-footed friends
For the duck may be somebody’s mothers.
Be kind to your friends in the swamp
Where it’s alwaaaaaas damp.
You may think that this is the end
Well it is.
I remember all of these schoolyard rhymes - they seem to have transmitted throughout the world in the days before the benefit of mass-media ( a very comforting thought).
How about the pranks then?
For example, Back in the days before global dissarmament, we were allowed to purchase home-explosives in one week of each year for “cracker-night” In my home town, cracker-night was a night on which we would light bonfires and stand around them letting-off “crackers” and sky-rockets. This has all been banned and digitally extracted from history. In fact, even mentioning it here will cause delays on C&F while the real-web-owners microscope every byte for terrorist activity (they are all secret ITM enthusuasts so we will feel the full force of it - much the same as the attraction the boy-scouts have for pedaphiles {c’mon guys - just enjoy the music damnit}). Opps wrong forum …
Anyway - how about this prank: - get a large “cracker” (we used to call them “tuppeny-bungers” - they were too strong for even brave idiots to detonate while held by the fingertips - however, you could get a nice launch by standing on an iron bucket with a tupnny bunger underneath)
… so get the cracker and affix it to the inside of a school toilet using chewing-gum with about half the cracker submerged and the wick clear of the water - get a cigarette and drill a hole through it about halfway - thread the wick of the cracker through the hole so wick and ciggy are all suspended above the water-line. When the bell sounds for everyone to line-up at assembly or to go to classes - light the cigarette - 4-5 minutes later, when everyone are safely away from the scene, a loud bang and puff of smoke are heard - the teacher or official sent to investigate finds a lot of smoke and the toilet bowl sheared-off at the water line. My father used to speak wisfully of a thing called a “basket-bomb” that was, reputedly 4 times as strong as a tuppeny-bunger … sigh …
To get this kind of fun in this day and age, you have to make active links with suppliers of cemtex on the black market ( a little more difficult than the old days, but not impossible - there are still gun-clubs that license the distribution of a thing called “Smokeless-powder” damn good stuff!).
So much for prohibition in all its forms 
(now about the effective grenade made with 6 boxes of matches, a church-candle and an A5 piece of paper … erm … 
perhaps not)
Any other similar pranks?
a (still) perfectly legal way to make a huge noise is with dry ice.
Take a pellet or two of dry ice and put it in an empty plastic soda bottle. A tiny amount of water. Screw the cap on tightly, then place in the sun.
Granted, the timing is a bit tricky - but when it goes - IT GOES! Watch out for shrapnel.
If you can’t find “legal” fireworks - you can still purchase black powder (for reloading) and the engines for model rockets. Different combinations of these also make for interesting effects.
And, yes, my kids are weird…
Yep, Rockets
I was so heartened to see the Mythbusters get access to “hobby” rocket engines more powereful than the military ones. Strong enough to push an old chevvy past the ton! And folks get jittery putzing about Nth Korea’s pathetic missile launches - any schoolboy could do that!
I got little ones and bunched them up - the thing is, the little jobbys have got a top-blow that ignites the next stage and separates the old one - you can cluster the little thangs enough to get some considerable altitude with about 4 stubby stages and some respectable velocities with some weighty payloads too - and it’s all made of cardboard and don’t show on radar (snigger).
(edited to say: Your kids are perfectly normal healthy humans!)
Be kind to your web-footed friends
For a duck may be somebody’s mother.
Be kind to your friends in the swamp
Where the weather is cold and damp - to rhyme with swamp.
You may think that this is the end
Well it is, but just to show that I’m a li-----ar,
I’m going to sing it again,
But only this time I will sing it somewhat higher.
Be kind etc. ad lib, as high as your voice will go.
No matter how young a prune may be
He’s always full of wrinkles.
A baby prune is like his dad
but he’s not wrinkled quite so bad.
We have wrinkles on our face
(falsetto) A prune has wrinkles everyplace.
No matter how young a prune may be
He’s always full of wrinkles.