World Development Indicators - Key Development Data & Statistics is an excellent tool for finding country statistics. It is a less confusing public part of very detailed tables and time series in the full database World Development Indicators Online
World Bank - "the World Bank is a vital source of financial and technical assistance to developing countries around the world, .....not a bank in the ordinary sense but a unique partnership to reduce poverty and support development"
Europa World is useful for an overview of a country from both an economic and a political history standpoint. It gives fairly current statistics for a country. Tables of "Country Statistics / Health and Welfare" for countries summarize statistics from the WHO and World Development Indicators sources, below.
Eurostat. Your key to European statistics.
Global Health Observatory (GHO) has statistical and news information on the 193 member countries. The World Health Organization (WHO) Statistical Information System (WHOSIS) has been incorporated into the Global Health Observatory (GHO) to provide you with more data, more tools, more analysis and more reports.
Global Insight provides comprehensive economic, financial, and political coverage of countries, regions, and industries -- covering over 200 countries and spanning more than approximately 170 industries.
CIA World Factbook "provides information on the history, people, government, economy, geography, communications, transportation, military, and transnational issues for 266 world entities."
UN Water Statistics and articles on international water issues, particularly concerning access to fresh water.
International Financial Statistics Online has detailed financial statistics
Monthly Bulletin of Statistics (United Nations) The United Nations is one of the main sources of statistics gathered from countries.
Britannica.com World Data Analyst is useful for statistical country rankings and direct comparisons as well as quick country overviews