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.
Integrated Public Use Microdata Series (IPUMS) International
The IPUMS International project at the University of Minnesota provides access to microdata samples from population censuses in dozens of countries from different regions and income categories and includes both the original data and harmonized variables for easier comparison over time and/or across countries. See https://international.ipums.org/international-action/sample_details for a list of the available samples.
International Household Survey Network (IHSN)
The IHSN is devoted to improving "the availability, accessibility, and quality of survey data within developing countries, and to encourage the analysis and use of this data by national and international development decision makers, the research community, and other stakeholders." As part of this mission, the IHSN has developed a very useful catalog of household surveys that covers both national and international surveys. The catalog allows users to filter by country, date range, and availability, and to search through variable descriptions and question texts.