"The Indian Census is the largest single source of a variety of statistical information on different characteristics of the people of India. With a history of more than 130 years, this reliable, time tested exercise has been bringing out a veritable wealth of statistics every 10 years, beginning from 1872 when the first census was conducted in India non-synchronously in different parts. To scholars and researchers in demography, economics, anthropology, sociology, statistics and many other disciplines, the Indian Census has been a fascinating source of data. The rich diversity of the people of India is truly brought out by the decennial census which has become one of the tools to understand and study India." [From the 2009 version of the Government of India census website.]
The earliest Census in modern form was undertaken in the late 1860s through 1871. The official Government of India Census website describes predecessors and general history here. See also the Bibliography of Census Publications in India, cited below, for everything published up to 1972.
Emory has various proportions of the Census of India reports.
Here is a sampling of resources from a search in DiscoverE for "Census of India."