Country Analyses - Analyzes a country's political, economic, social, and technological structure as well as its history
Freedom House - A good source of information on political rights and civil liberties in countries around the world. In addition to ranking countries, they also have some excellent country profiles that describe the political situation in each country/territory that they rank.
Human Development Index - Provided by the UN, it covers the advancement in humanity
World Factbook - The website provides a basic overview of the countries
World Bank Data - Datasets that cover political science issues
Polity - The most widely used measure of democracy in political science research
The Global State of Democracy - Allows you to look at where countries are based on democracy indices, compare those numbers to other countries, and see how those numbers have changed over time
Varieties of Democracy - A common tool for measuring democracy (users can also use it to create their own custom measures for countries)
World in Data: Democracy - Show empirical evidence about the change in democracy over the years
Civil Wars - Has charts about various Civil War and offers some insight as to why these wars happen
Civil Wars since 1945 - This Wikipedia article provides good background knowledge to help you see what wars were going on
Economic Growth - Offers an overview of economic growth of major countries through the years and concrete data to help back those claims up
Imports and Exports - From the US government, this offers a list of a country's major imports and exports and how the effects their economies
Observatory of Economic Complexity (OEC) - This website tracks the exports and imports of countries around the word and presents this data in some fairly easily digestible profiles