The name was quite fashionable throughout the English-speaking world from the beginning of the 18th-century all the way up until the turn of the 20th-century.
The highest Harriet ever ranked in U.S. naming history was in 1880, coming in as the 73rd most popular female name. As of 2010, she does not even appear in the U.S. top 1000.
Harriet was the 86th most popular female name in England/Wales, (2010).
The name has been borne by several famous personages, including, Harriet Beecher Stowe (1811-1896) and Harriet Tubman (1820-1913).