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. (Also in print at Paley Reference Desk at call number D2 E822.
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.
OECD iLibrary Statistics primarily on 30 of the most developed countries with some additional coverage.
GeoHive: Global Statistics World population statistics and links to world statistical agencies. The Country Data Index often links to country statistics by district for last 10 year span available and to the official national source of statistics.
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
International Financial Statistics Online has detailed financial statistics
LexisNexis Statistical is a tool for finding statistics from all over the world.
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