I've had a great idea from someone who suggested I mention rhyming sites for kids. The website she recommended is http://kidsfront.com/rhymes-for-kids.html called Rhymes for Kids, Short Rhymes, Nursery Rhymes - Kidsfront.com. This site offers many short rhymes you may remember singing as a child.
Other sites for rhymes are http://www.zelo.com/family/nursery/ for Mother Goose Nursery Rhymes; http://www.rhymes.org.uk/ which has Nursery Rhymes, lyrics, orgins and history, and includes a trivia quiz (very interesting!); and http://www.smart-central.com/, where you can select rhymes from a drop down menu based on alphabetical order by title.
Answers.com, defines nursery rhyme as follows: a traditional verse or set of verses chanted to infants by adults as an initiation into rhyme and verbal rhythm. Most are hundreds of years old, and derive from songs, proverbs, riddles, ballads, street cries, and other kinds of composition originally intended for adults, which have become almost meaningless outside their original contexts. Their exact origins are often obscure, although a few more recent examples are by known authors: ‘Mary had a little lamb’ was written by Sarah Josepha Hale in 1830. See also jingle, nonsense verse.