As of July 2013, currency in circulationthat is, U.S. coins and paper currency in the hands of the publictotaled about $1.2 trillion dollars.
The amount of cash in circulation has risen rapidly in recent decades and much of the increase has been caused by demand from abroad.
I'll challenge that. Over the recent decades we've seen the widespread adoption of credit and debit cards and in the last ten years that's turned to online payments. The volume of cash, i.e., paper money, used in the last decades has declined significantly.
EDIT: I stand corrected. Just found
this article from the New Yorker which claims the amount of US paper currency in existence has increased. This is must be an indicator of how much the money supply has increased over the same time period...because the developed world has certainly shifted to a more electronic payment system.