The Statistical Abstract of the United States is a great compilation of national statistics from many sources -- government and private. It also is used as an index, or finding tool, to find the source of the statistics.
The U.S. Census Bureau provides local, state and national statistics relating to poverty, educational attainment, overcrowded housing, single parent families, grandparents raising grandchildren, etc. Much of the data can be "cross-tabulated" by another variable such as race/ethnicity, gender, immigrant status, language or age. Data.census.gov is the main entry point. Social Explorer can be used to create interactive thematic maps from census data.
A number of sites offer datasets that may be downloaded and manipulated using standard statistical applications such as SPSS, SAS or STATA.
Inter-University Consortium for Political and Social Research Consortium of 325 institutions working together to acquire and preserve social science data in 130 countries. Includes survey data, census records, election returns, economic data, and legislative records.
National Archive of Computerized Data on Aging Located within ICPSR, funded by the National Institute on Aging. Offers data relevant to gerontological research.
Social Science Data Archives - North America Directory for datasets in the social sciences.
Substance Abuse and Mental Health Data Archive (SAMHDA) Public use data files for substance abuse and mental health research.
UCDATA UC Berkeley's principal archive of social science data and statistics. Presents statistical datasets covering many social science areas, plus reports and statistical analyses.