Climate Change and African Political Stability (CCAPS)
http://www.strausscenter.org/ccaps/
The CCAPS project, which is hosted by the Strauss Center for International Security and Law at UT-Austin, is devoted to the study of the relationship between climate change and international/internal stability on the African continent. The project has produced various data collections such as the Social Conflict Analysis Database (SCAD), which provides event-level data on riots, coups, strikes, and other instances of social unrest, and the Armed Conflict Location and Event Dataset (ACLED), which provides event-level data on various types of armed conflict.
Education Policy and Data Center
https://www.epdc.org/
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
https://data.worldbank.org/topic/gender
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 Health Data Exchange (GHDx)
http://ghdx.healthdata.org/
The Global Health Data Exchange is an undertaking by the Institute for Health Metrics and Evaluation (IHME) and is a "comprehensive catalog of surveys, censuses, vital statistics, and other health-related data." While it is not a data archive and thus does not necessarily provide access to specific data resources, it is a very useful tool for locating health/demographic data at both the micro- and macro- levels. The IHME has various other data-related projects, including its estimates of Global Burden of Disease.
Health, Nutrition and Population Data and Statistics
https://datatopics.worldbank.org/health/
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)
https://data.humdata.org/
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.
OECD Query Wizard for International Development Statistics (QWIDS)
https://stats.oecd.org/qwids/
QWIDS is a (relatively) accessible interface for very detailed data on foreign aid and development assistance that allows you to break down aid flows by combinations of recipient, donor, and purpose of aid.
Quality of Government (QOG) Institute
https://www.gu.se/en/quality-government
The QOG Institute is hosted by members of the Department of Political Science at Göteborg University in Sweden and is devoted to "the causes, consequences and nature of 'good governance.'" The Institute has created multiple collections of data on governance: a broad collection of governance indicators that is global in coverage; a more narrow collection that focuses on social policy in wealthier countries; data from expert surveys on politicization and professionalization of public administration in individual countries, and a new data collection on perceptions of corruption in individual regions within EU members. The data are compiled from multiple sources, including the Polity Project, the Cingarelli-Richards Human Rights Data, Transparency International, Freedom House, various international organizations, and datasets produced by various academics. The QoG data are available in SPSS, Stata, and comma-delimited (.csv) formats.
World Development Indicators (World Bank)
https://datacatalog.worldbank.org/search/dataset/0037712
The World Development Indicators provide convenient access to hundreds indicators on over 200 countries and territories. Data are available annually from 1960 forward, with variation across countries and indicators. The database is part of the Bank's Data Catalog of statistical databases and other data collections. There are also multiple tools available for importing WDI data directly into programs such as R and Stata.