Virtually all nursery rhymes are either allegories or 'training songs' as it were.
Its not particularly well presented, but for a good outline of some, take a look at
http://www.wowessays.com/dbase/ad1/aym107.shtml
Note, the website's analysis of ring-a-ring-a-rosey uses the British / Australian variant, which goes atishoo atishoo we all fall down, and also has a claim that it could in fact be a hindu chant in any case. take a look.
Sadim
Thanks for the link to the essay on the origin of nursery rhymes. It was quite interesting!