The Scottish/Texan folksinger, Ed Miller, has been collecting a whole bunch of these playground favorites, and does a bunch of them in concert. (Is the original request from you, Ed? you didn't sign it...) He notes that he's heard variations of "Mine eyes have seen the glory of the burning of the school" both here and in Scotland. There's a classic line about a teacher; in Scotland (Glasgow, I think?) it goes:

"I hit her in the bean with a rotten tangerine,
And she ain't gonna teach no more!"

Here in the Land of the Free and the Home of the NRA it usually goes:

"I shot her from the door with a loaded 44,
And she ain't gonna teach no more!"

My memories of favorite playground ditties is sadly faded; the only one that has stuck (other than "Greasy, Grimy Gopher Guts) is a parody of a TV ad jingle, to the tune of Colonel Bogey's March:

"Comet, it tastes like gasoline;
Comet, it makes your hair (or teeth) turn green;
Comet, it makes you vomit,
So have some Comet, and vomit today!"

I like today's violent parodies of the sicky-sweet Barney song; there's lots of variations on this one.:

"I hate you, you hate me,
Let's go out and kill Barney,
And a shot rang out and Barney hit the floor,
No more purple dinosaur!"

These are fun; hope to see a lot more!