You may also want to check whether a particular country has a statistical agency similar to the U.S.'s Census Bureau. Such agencies often provide rich data resources on their web sites.
From the U.S. Census Bureau, this database provides basic population and demographic statistics for countries around the world.
Major source for data on the global economy, offering statistics on over 550 development indicators from over 200 countries. The data from WDI Online cover national economies, population, natural resources, financial matters, environmental variables, and much more, from 1960 to date. You can also export the data in formats such as Excel, and while in the database, perform such functions as view by percentage change and even chart the figures.
The Inter-university Consortium for Political and Social Research (ICPSR) is a large archive of social science data.