well, the way i learned it it went like this:

down by the river of the hanky panky
where the bullfrogs jump from bank to banky
singing hip hop dont stop
listen to the water drop
1 2 3 4 5 6 7 8 9 10

and then at ten one person trys to slap the other's hands.

i dont know how it goes in other places, but thats the way we say it in New England :)
hope it helped !