I have an early memory of sitting in a ring at kindergarten reciting Little Miss Muffett but the one I remember all the way through is Eency Weency Spider and I have taught it to many a young child since. There were a lot of ladybirds around when I was growing up and we used to put them on our hands and recite Ladybird, Ladybird fly away home.
Goodness, I know lots! Incy wincy spider, Little Miss Muffett, There was an old lady, Ladybird ladybird fly away home, Ladybird she creeps along, There's a worm at the bottom of the garden, The ants go marching two by two..... I'm sure there are more but those are the first to leap to mind :)