Ron Guth: The United States Three Cents is an unusual denomination that first appeared in 1851, although pattern coins for the denomination were produced in 1849 and 1850. The original purpose of the Three Cents coins to provide an intermediate denomination between the Cent and Half Dime, making it easier to change some of the odd foreign coins that were legal tender in America at that time. In 1851, postal rates were dropped from five to three cents. While three Large Cents could have been used to purchase a postage stamp, the bulky copper coins were expensive to produce. Thus, a coin of three cents value had two purposes, enough to get the denomination started in 1851.
In 1865, a "Nickel" Three Cents was introduced (the predominant metal in the coin was actually copper, but because the color was more whitish than brown, "nickel" was considered a better descriptor). These were minted side-by-side with the silver versions until 1873, when the silver type was discontinued. The nickel versions were minted until 1889, when the entire denomination was discontinued.
Several of the Nickel Three Cents were struck only as Proofs (1877, 1878, and 1886); other dates (such as 1884 and 1885) are represented by very few circulation strikes. Interesting varieties include:
1873 Open 3
1873 Closed 3
Sources and/or recommended reading:
"Base-Metal Instincts" by Jon Taylor, NUMISMATIST, December 2004, page 14