Negro, Black and African-American Census Reports: 1840

Overview - 1840 Census
Census Bureau

Index of Questions
Census Bureau 

(1841). Sixth census or enumeration of the inhabitants of the United States: As corrected at the Department of state, in 1840. Published, by authority of an Act of Congress, under the direction of the secretary of state. Washington: Printed by Blair and Rives.
[Free whites male and female: under 5, 5-9, 10-14, 15-19, 20-29, 30-39, 40-49, 50-59, 60-69, 70-79, 80-89, 90-99, 100 and older. Slaves and free colored: male and female: under 10, 10-23, 24-35, 36-54, 55-99, 100 and older]. 476 pages.
Census Bureau description only, no full-text
WorldCat 

Statistics of the United States of America, as collected and returned by the marshals of the several judicial districts, under the thirteenth section of the act for taking the Sixth Census. 409 pages.
Census Bureau description only, no full-text
WorldCat

Compendium of the enumeration of the inhabitants and statistics of the United States, as obtained at the Department of State, from the returns of the sixth census, by counties and principal towns, exhibiting the population, wealth, and resources of the country, with tables of apportionment. 379 pages.
Census Bureau
WorldCat

Census of Population and Housing
Volume 3. Compendium of the Enumeration of the inhabitants and statistics of the United States, as obtained at the Department of State, from the returns of the Sixth Census...To which is added an abstract of each preceding census.
Title Page [PDF], Full Document [ZIP, 223.5 MB]
Census Bureau

A Census of Pensioners for Revolutionary or Military Services. 195 pages.
Census Bureau

United States., Cummings, J., & Hill, J. A. (1969). Negro population in the United States, 1790-1915. New York: Kraus Reprint. 844 pages. : illus., maps. Reprint of 1918 edition.
Hathi Trust 
WorldCat 

McKenney, N. D. R. (1979). The social and economic status of the Black population in the United States: An historical view, 1790-1978. Washington: U.S. Dept. of Commerce, Bureau of the Census. Current Population Reports, Special Studies, Series P-23, No. 80. 270 pages.
ERIC (full-text)
WorldCat

Black Demographic Data, 1790-1860: A Sourcebook. Westport Conn: Greenwood Press. 
WorldCat

This map of the United States illustrates the nation's population density using 1840 census data. (link)

City population 1840 (link)