Association of Religion Data Archives (ARDA)
The ARDA contains many datasets pertaining to religion, including both surveys on religious attitudes and data on denominations and denomination membership. While ARDA's focus is mainly on the United States, it also provides national profiles of the religious compositions of individual countries and cross-national datasets covering topics such as religious freedom, estimates of populations by religion, and relations between the state and religion more generally.
Demographic and Health Surveys (DHS)
The DHS is a project funded by the United States Agency for International Development to promote better gathering of survey data on health issues pertaining to family life and reproductive health in developing countries. Aggregated data from DHS surveys are readily accessible via the STATcompiler interface that allows for on-line visualization and for download in tabular form. Microdata files from the surveys are also available upon registration and application for access. The University of Minnesota's IPUMS project has also produced the IPUMS DHS collection of harmonized extracts of data from DHS surveys.
Education Policy and Data Center
The Education Policy and Data Center provides access to education measures and indicators from a range of sources such as administrative records, household surveys, and assessment tests. Users can search for data by country, topic, or level of education.
Gender Equality Data and Statistics
The World Bank's collection of gender-equality data is "a one-stop shop for gender information, catering to a wide range of users and providing data from a variety of sources." Amongst the resources here are collections of macro- and micro-level data on topics such as control of economic assets and financial inclusion and an extensive set of gender-themed indicators that can be downloaded in bulk or queried by country, year, and indicator.
Global Multidimensional Poverty Index (MPI)
Oxford University's Oxford Poverty and Human Development Initiative produces the Global Multidimensional Poverty Index, which is "an international measure of acute multidimensional poverty covering over 100 developing countries." The index is constructed from data on nutrition, child mortality, education, and measures of standard of living such as access to drinking water and household assets. County profiles include sub-national breakdowns, and data tables have MPI estimates back to 2010 (varying by country).
Health, Nutrition and Population Data and Statistics
HealthStats is "the World Bank’s comprehensive database of Health, Nutrition and Population (HNP) statistics," covering topics such as reproductive health, population growth, communicable and non-communicable diseases, and health facilities. The data are accessible through various means, such as via an interface that allows for both queries and bulk downloads and via tools to break health data down by household wealth.
Humanitarian Data Exchange (HDX)
The Humanitarian Data Exchange is a very helpful catalog of data resources that will let you search for or filter resources by combinations of topics and locations and provide information about how the data can be accessed.
World Bank Poverty and Equity Data
The World Bank has brought together a variety of datasets pertaining to the study of poverty, income inequality, and income distribution, along with other resources relevant for international development and economics. The many potentially-useful resources listed within this site include the World Income Inequality Database and PovcalNet. The site is part of the Bank's broader collection of poverty indicators. Other data resources are available via the Bank's Poverty and Inequality Research Progam and via the Bank's Data Catalog. Be warned - the World Bank tends to change addresses for websites without warning.
World Population Prospects
This database is produced by the United Nations' Population Division and contains cross-national data on basic population demographics and vital statistics (e.g. birth and death rates, maternal mortality, population by age and gender and urban/rural areas, median age of population). See https://www.un.org/en/development/desa/population/publications/dataset/index.asp for other data from the Population Division, cover topics such as migration, fertility, marital status, and population policies.