Brief, factual profiles.

A standard source for brief country profiles ...

From the Canadian Foreign Service Institute of Foreign Affairs and International Trade. It has a Q & A format.

From the US Dept of State, information about travel: entry/exit requirements, any travel warnings, and more.

These are the profiles that succeed the Country Studies / Area Handbook Series (see next link). Not nearly as lengthy, nor are as many countries covered, but the reports are more current.

These are online books. They were originally sponsored and published by the U.S. Department of the Army between 1986 and 1998. At present, 101 countries and regions are covered. Each study offers a comprehensive description and analysis of the country or region's historical setting, geography, society, economy, political system, foreign policy, and national security.

From the U.S. Energy Information Administration.
These reports and notes provide information on a country's energy production and/or energy usage. For 39 energy producing countries, the Country Analysis Briefs include: total and crude oil production, oil consumption, natural gas production and consumption, coal production and consumption, electricity generation and consumption, primary energy, energy intensity, CO2 emissions and imports and exports for all fuels.

These reports from the International Monetary Fund tend to be more in-depth and topical.

For free data in particular, look at their World Economic Outlook database.
We also subscribe to their online data database International Financial Statistics.

Browse data on the four big themes that UNESCO tracks (Education, Literacy, Science & Technology, Culture & Communication)

This is UNESCO's data extraction website.

Here you'll find data on several aspects of economic activity in a country, including trade and employment data.

Here you'll find tabular data on countries by theme. Some data are in downloadable spreadsheets. Much of this data corresponds to the UN's Demographic Yearbook.

The World Bank has recently made lots of their data available free. This includes their World Development Indicators, Global Development Finance, African Development Indicators, and more.

This agency works to "advance U.S. national security, foreign policy, and economic objectives by ensuring an effective export control and treaty compliance system and promoting continued U.S. strategic technology leadership."

GATS stands for 'Global Agricultural Trade System'. It provides international agricultural, fish, forest and textile products trade statistics dating from the inception of the Harmonized coding system in 1989 to present. Also includes BICO (Bulk, Intermediate, and Consumer-Oriented) reports.

Provides data on exports of small and medium-sized firms ... data on exports from US metro areas and their trade partners and more.

ITA is part of the US Dept. of Commerce. Lots of data here ...

Also from the OTII, data on US exports at the national and state levels. This is a neat site that allows mapping ...

Registration required for at least parts of the site. This is the EU's main statistical site.

UNCTAD and the WTO produce this site.

Look for the Composition of Trade tables ...

Includes imports and exports data, some commodity pricing, and more.

From the United Nations Conference on Trade and Development. Has data for trade, commodities, economic trends, FDI, maritime transport, and more.

From the WTO (World Trade Organization).

Parts of this site are not free access, but there's still a lot of information that is readily accessible. Includes a trade barriers database (http://mkaccdb.eu.int/madb_barriers/barriers_select.htm)