I thought of a few more:

(A clapping game that we used to have contests at recess with. Everyone stood in a circle and you had to move your hand out of the way before you got hit on "boo", otherwise you were out. When it got down to two people, it became a sort of tug of war.)
Down by the riverside, the hanky panky side
East side, West side, hanky panky side
A E I O U Bamboo!

(Another clapping game)
A sailor went to sea sea sea
to see what he could see see see
But all that he could see see see
Was the bottom of the great blue sea sea sea

Some bus songs:
"There was a bear..."

Bubblegum song "My mommy gave me a penny, and told me to buy a henny...)

A ricky bamboo (a ricky bamboo)
Now what is that? (now what is that?)
It's something made (it's something made)
By the Princess Pat (by the Princess Pat)
It's red and go-old (It's red and go-old)
And purple, too (and purple, too)
That's why it's CALLED! (that's why it's CALLED!)
A ricky bamboo (a ricky bamboo)
Now Captain Jack (now Captain Jack)
Had a mighty fine crew (had a mighty fine crew)
He sailed across (he sailed across)
The ocean, too (the ocean, too)
But his ship did sink (but his ship did sink)
And yours will, too (and yours will, too)
If you don't HAVE! (if you don't HAVE!)
A ricky bamboo (a ricky bamboo)
[repeats from the top]