It's thought by many that this rhyme is over 300 hundred years old, and was taught to children to make them aware of the London plague:
Ring a ring of roses (A rosy rash, in circles, was a symptom of the plague)
A pocket full of posies (Posies of herbs were carried as protection)
Atishoo, atishoo, we all fall down (Sneezing was thought to be the fatal symptom, we all fall down dead)
People still say 'bless you' when people sneeze, as they did in 1665 at the time of the London plague.
They're are experts on folklore who disagree that the nursery rhyme came about as a result of the plague, but...? It's still interesting methinks!