Greenback
  
For most of the early part of American history, the U.S. had no national paper currency. People who wanted to use money could use various foreign currencies, if they could get people to accept them. Or they could use what's called specie, gold or silver (often minted into coins). Or they could use bank notes, whose value depended on the bank and how far away the institution was located.
Then came the Civil War. To pay for the massive expense, the U.S. issued its first paper currency, the greenback (thus called because the printing on the back was literally green).
These notes were only issued for a few years during the war (which took place from 1861-1865, for those of you who flunked U.S. history). However, the color scheme stuck. When a more permanent paper currency came into play, it kept the green printing of the Civil War currency. Thus, the term "greenback" has remained a nickname for U.S. currency.