The United States has produced several coins and banknotes of its dollar which no longer circulate or have been disused. Many of these were removed for specific reasons such as inflation reducing their value, a lack of demand, or being too similar to another denomination.
Coinage
There have been numerous coins throughout the United States dollar's history that no longer circulate. Some, like the half-cent coin were removed due to inflation reducing their value while others such as the two-cent piece were removed due to a lack of demand.
Note that this table shows the latest status before the coin denomination was rendered obsolete.
References
Obsolete denominations of United States currency Wikipedia(Text) CC BY-SA