From the Asymptosis post:
The Continental Currency was plagued, though, by increasing public distrust. The Continental paper dollar was able to hold its value at par with a specie dollar only until October, 1777, by which time widespread counterfeiting by British, Tories, and opportunists conspired with the natural inflation of a printing press economy and increasing uncertainty as to the outcome of the war to push the exchange ratio of the Continental Currency to $11 in paper for $10 in specie.
After that point the devaluation accelerated. By the next year, October, 1778, the ratio was 4.66 to 1.
The low point was reached in April, 1780, when a dollar in silver or gold was worth $40 Continental. And these were the official exchange ratios adopted by the Congress...
Issued current with the Colonial and Continental currencies were numerous privately-sponsored paper monies emitted by banks (as early as 1732 in Connecticut), utilities, merchants, individuals and even churches.
These issues continued after the Revolutionary War, and proliferated in the 19th Century...
The tens of thousands of privately-issued bank and scrip notes of the 1800s ranged in denomination from one-half cent to several thousand dollars. While today their collector value depends on a combination of rarity, condition and demand; their value when issued was solely dependent on the reputation of the issuing authority -- be it bank, railroad or Main Street apothecarian.