EDIT MAIN
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CIA World Factbook

Amnesty International

United Nations Economic & Social Council

Also the main site has a list of issues & campaigns with links:

ISSUES / CAMPAIGNS


BBC News Country Profiles

Country profiles also looks at the current leader(s), a brief timeline of important dates, a link at the bottom "Related Topics - [Country name]" that takes the user to other recent newsworthy events regarding that country. 
Example Afghanistan profile

United Nations Association provides a whole page of Country Information Links. 

The U.S. Bilateral Relations Fact Sheets

InfoPlease

Model United Nations Manifesto <<insert document link>>

The New York Times
News by Country pages:
Go to each region, then scroll about halfway down on the right to "Times Topics: Find News by Country"