According to Wiki, in Middle English, "pygg" referred to a type of clay used for making various household objects such as jars. People often saved money in kitchen pots and jars made of pygg, called "pygg jars". By the 18th century, the spelling of "pygg" had changed and the term "pygg jar" had evolved to "pig bank", and what we have now.
Wikipedia also tells me piggy banks are most often, but not exclusively, used by children. I'm not quite sure what that says about me.
P.S. As you can tell, it's only about 1/3 full with coins, and a couple dollar bills, which is probably less than I had as a child. Definitely not worth sneaking into my house to steal it away from me. The gas to get there will probably cost you more than what you'd find in the bank. :)