Directly copied from http://www.moneyfactory.gov/faqlibrary.html

Why were certain individuals chosen to be pictured on our paper currency?

The Secretary of the Treasury is responsible for the selection of the designs, including the portraits, which appear on paper currency. The July 11, 1862 Act of Congress provided: "That the Secretary of the Treasury be, and is hereby authorized, in case he shall think it expedient to procure said notes, or any part thereof, to be engraved, printed, and executed, in such form as he shall prescribe, at the Treasury Department in Washington, and under his direction; and he is hereby empowered to purchase and provide all machinery and materials, and to employ such persons and appoint such officers as may be necessary for this purpose."

The portraits currently appearing on the various denominations of paper currency were adopted in 1929 when the size of the notes was reduced. Prior to the adoption of this smaller sized currency, a special committee was appointed by the Secretary of the Treasury to study this aspect of the design. It was determined that portraits of Presidents of the United States have a more permanent familiarity in the minds of the public than any others. This decision was somewhat altered by the Secretary of the Treasury to include Alexander Hamilton, who was the first Secretary of the Treasury; Salmon P. Chase, who was Secretary of the Treasury during the Civil War and is credited with promoting our National Banking System; and Benjamin Franklin, who was one of the signers of the Declaration of Independence. All three of these statesmen were well known to the American public. Treasury Department records do not reveal the reason that portraits of these particular statesmen were chosen in preference to those of other persons of equal importance and prominence. By law, only the portrait of a deceased individual may appear on U.S. currency and securities. Specifics concerning this law may be found under United States Code, Title 31, Section 5114(b).