The CIA World Factbook will give you quick stats about population, religion, and a brief background on economics
Background Notes from the US State Department will give you complementary information
BBC News also has Country Profiles
Doing Business has country and economy profiles
Index of Economic Freedom by the Heritage Foundation, ranks over 180 countries on economic freedom and prosperity
International Data Base (IDB) - The US Census Bureau's publication on national and world population data with country rankings dating back to 1950 and projections through 2050.
International Statistics Agencies - a list of agencies from other governments. Look for your country here.
World Development Indicators, an online book from the World Bank
Executive Planet has etiquette tips
As does this Intenational Business site
The subscription database Business Source Complete (linked off of http://www.galileo.usg.edu/scholar/westga/databases/b/) has documents called "Political Risk Yearbooks" for most countries
BrazilTradeNet - from the Brazilian government (English)
Ministério de Desenvolvimento, Indústria e Comércio Exterior (Brazilian government page in Portuguese)
Secretary of Economy from Mexico (English)
Ministry of Commerce, People's Republic of China (English)
French Ministry of Foreign Trade (English)
Germany Trade and Invest (English)
Department of Commerce, India (English)
Ministry of Trade, Economy and Industry, Japan (English)
Ministry of Industry and Trade, Russian Federation (English)
Ministry of Industry, Tourism and Trade, Spain (English)
Department of Enterprise, Trade and Industry, UK (English)