Here are a list of popular statistical resources providing free datasets:

•  American FactFinder
  U.S Census Bureau statistics for Population, housing, economic and geographic data for states, cities and towns.Access to the decennial censuses, the American Community Survey and the Economic Census.

• Data.Gov
  This US Governmental site aims to improve public access to high value, machine readable datasets generated by the Executive Branch of the Federal Government. Here, you can find data, tools, and resources to conduct research, develop web and mobile applications, design data visualizations, and more.

• Data-Planet
  Provides access to statistical data produced by U.S. Federal agencies, States, private organizations, and major intergovernmental organizations. There are up to 2 billion charts, maps, views, rankings, time series and tables available for use in the Data-Planet repository. Link to Ready Reference interface.

•  General Social Survey
  The GSS contains a standard ‘core’ of demographic, behavioral, and attitudinal questions, plus topics of special interest. Many of the core questions have remained unchanged since 1972 to facilitate time-trend studies as well as replication of earlier findings. The GSS takes the pulse of America, and is a unique and valuable resource. It has tracked the opinions of Americans over the last four decades.

• Integrated Public Use Microdata Series (IPUMS)
  Consists of more than fifty high-precision samples of the American population drawn from fifteen federal censuses and from the American Community Surveys of 2000-2011.

• The Inter-University Consortium for Political and Social Research (ICPSR)
  The Inter-University Consortium for Political and Social Research. World’s largest archive of social science data. Election data, opinion polls, more. Special collections on Health, Education, Aging, Crime, Substance Abuse. A great place to begin looking for raw data. Many dataset files come formatted for major statistical packages (Stata, SPSS, SAS).

• iPoll Databank
  Includes all survey data for which the Roper Center holds the datasets as well as survey data from Pew Resarch Centers, Kaiser Family Foundation, Gallup Organization and more.

• IQSS Dataverse
  Data repository hosted by Harvard University containing raw data files of interdisciplinary research studies in both the sciences and social sciences

• OECD iLibrary
  OECD iLibrary provides online access to Organisation for Economic Co-operation and Development (OECD) resources, covering trade, environment, agriculture, technololgy, economic development, and more. The books, reports, working papers and periodicals are full-text and the databases have extensive statistical information.

• Policy Map
  Mapping tool much like Social Explorer but integrates other data sources from the Department of Homeland security, Bureau of Labor Statistics and the U.S Census

• ProQuest Statistical Insight
  Provides access to statistics and tables in reports produced by federal agencies, states, intergovernmental organizations as well as private enterprise.

• re3data.org
  Searchable catalog of research data repositories

• Roper Center
  The Roper Center for Public Opinion Research is one of the world’s leading archives of social science data, specializing in data from surveys of public opinion. Includes over 18,000 datasets across many subjects.

• Social Explorer
  Interactive visualization tool that utilizes the decennial censuses and American Community Survey data. Also includes select data sets on crime, religion, recent presidential approval ratings and more. Can be used to visually study demography and change over time in the United States.

• UNdata
  Official statistics produced by countries and compiled by United Nations data system, as well as estimates and projections. The domains covered are agriculture, education, energy, industry, labour, national accounts, population and tourism. Largest aggregator of international data. If you’re looking for data from different countries this is a good place to start.

   To collect, analyze, publish, and disseminate information on crime, criminal offenders, victims of crime, and the operation of justice systems at all levels of government. These data are critical to federal, state, and local policymakers in combating crime and ensuring that justice is both efficient and evenhanded.
• The Bureau of Justice Statistics (BJS)
  To collect, analyze, publish, and disseminate information on crime, criminal offenders, victims of crime, and the operation of justice systems at all levels of government. These data are critical to federal, state, and local policymakers in combating crime and ensuring that justice is both efficient and evenhanded.
• FBI Uniform Crime Reports (UCR)
  “The Uniform Crime Reporting (UCR) Program has been the starting place for law enforcement executives, students of criminal justice, researchers, members of the media, and the public at large seeking information on crime in the nation. The program was conceived in 1929 by the International Association of Chiefs of Police to meet the need for reliable uniform crime statistics for the nation. In 1930, the FBI was tasked with collecting, publishing, and archiving those statistics.”
  The UCR tool extracts state and local agency statistics on violent and property crimes. The “Crime in the United States” reports often have data tables available for download as well.
• Countrydata.com (PRS Group)
  Over 75 variables for more than 150 countries including ratings and data from the International Country Risk Guide and Coplin O’Leary PRS Forecast. Updated monthly with archives back to 1984. Note: CountryData offers spreadsheet data only. For PRS text and analysis, see International Country Risk Guide and Political Risk Services, both found in LexisNexis.
• Air Data (EPA) 
  AirData provides annual summary air pollution data for the United States.
• Center for International Earth Science Information Network 
  The Center for International Earth Science Information Network (CIESIN) was established in 1989 as an independent non-governmental organization to provide information that would help scientists, decision-makers, and the public better understand the changing relationship between human beings and the environment. Contains datasets by subjects: agriculture, climate, conservation, governance, hazards, health, infrastructure, land use, marine and coastal, population, remote sensing, sustainability, urban and water.
• OECD iLibrary
  International statistics on energy sources and energy policy
• The Little Green Data Book (World Bank)
  The Little Green Data Book is a pocket-sized ready reference on key environmental data for over 200 economies. Key indicators are organized under the headings of agriculture, forestry, biodiversity, energy, emission and pollution, and water and sanitation.
• U.S Energy Information Administration
  Provides tables on U.S energy prices, petroleum, natural gas, electricity, coal, renewable energy, and C02 emissions
• World Resource Institute Datasets
  Contains datasets on greenhouse has emissions and other climate-relevant indicators.