The Afrobarometers are an ongoing series of surveys conducted amongst countries in sub-Saharan Africa, focusing on topics such as political participation, national identity, civil society, and other such topics. Data from the Afrobarometers are available from the project site and also via the ICPSR.
The Arab Barometers are a series of surveys conducted in MENA countries to measure social attitudes on topics such as religiosity, national identity, trust in political institutions, and political reform. Data from the waves of the Arab Barometer are available via the ICPSR and via the Arab Barometer project site. The project site also has an interface for basic analysis of the data.
Association of Religion Data Archives (ARDA)
The ARDA contains many datasets pertaining to religion, such as surveys on topics such as the public's religious attitudes and practices, surveys of church leaders, and studies on the provision of social services by individual congregations While the focus of the archive is on the United States, ARDA also has many international surveys as well. See the Data Archive for the full list of available surveys and data.
Economic Research Forum
The Economic Research Forum is a research institute focusing on economic policy and development, with a focus on Egypt and other countries in the MENA region. In addition to its research, the Form also has a data archive of surveys and firm-level data covering topics such as labour market participation, household income and consumption, access to credit, and foreign trade. See https://erf.org.eg/erf-micro-data-catalogue-nada/ for information about accessing datasets from the archive.
World Values Surveys Series
The World Values Survey is "a worldwide investigation of sociocultural and political change. It is conducted by a network of social scientist at leading universities all around world. The survey is performed on nationally representative samples in almost 80 societies on all six inhabited continents." It is an excellent source for cross-national survey data and is a widely-referenced resource.