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.
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.