Thank you David Weingart for the new version of the persistant spider
song.  Another nursery rhyme that's been around for aeons is

THREE RODENTS WITH OPTICAL DEFICIENCIES
(CREDIT OR BLAME TO UNA K OWEN AND ANN ONYMOUS)

Three rodents with optical deficiencies
Three rodents with optical deficiencies
See how they perambulate
See how they perambulate
They all perambulated after the agriculturists spouse
Who amputated their cocxycal appendage with a carving utensil
Have you ever observed such an occurence in your sphere
As three rodents with optical deficiencies.

Also:
Row row row your boat
Underneath the stream
ha ha fooled you
I'm a submarine.

From "Singout" 
McDonalds is your kind of place
Hamburgers in your face
French fries up your nose
Pickles between your toes
Ketchup running down your back
I want my money back 
Before I have a heartattack.
(This was in a column by the really great male folksinger who was in a
car accident a number of years back, and came back to full function
after many many years.)