Whether you're performing research about a particular country for your latest class assignment, planning a trip, or just wishing to understand more about the countries that you hear about in the news, you will definitely benefit from some of these web sites!
The CIA World Factbook (https://www.cia.gov/library/publications/the-world-factbook/) provides up-to-date facts about countries. (Information from the 2013-14 Edition is currently available. If you need to check about the date updated in the future, select About, and then select Copyright/Contributions for that information.) The Factbook will provide you with summary information and a huge variety of statistics for your chosen country.
The State Department Countries & Regions page (http://www.state.gov/countries/) keeps a variety of information on countries, including press releases, information about relations with the US, passport/visa information, travel warnings, and more. Simply browse the regions or select the country that you're interested in under General Information, A-Z List of Countries and other Areas. If you're planning to travel and would learn more about things like visa and vaccination requirements, take a look at the Bureau of Consular Affairs page (http://travel.state.gov/content/passports/english.html) and select your country.
For in-depth historical information you might want to take a look at the Library of Congress's Country Studies web site (http://lcweb2.loc.gov/frd/cs/cshome.html). However, be cautious about the other facts and statistical information from this site, because most of these pages have not been updated since 1989-1998! (Lack of funds.)
Sometimes, you might want to get information directly from the country that you're researching. In these cases, consider looking at their Embassy web pages. The State Department provides a list of these pages for quick access at http://www.state.gov/s/cpr/rls/dpl/32122.htm.
Whether you visit these countries in person or virtually, have a great trip!
35 minutes ago