How can I research the risks (political, etc.) associated with doing business in specific countries around the world?
Take a look at this guide from the Pomerantz Business Library. It contains links to resources such as Business Monitor Online which provides quarterly reports on specific countries. In addition, there are also links to CountryWatch and CIA WorldFactbook both which provide good general information on the history, demographics, government, etc. for countries around the world.
It is also worthwhile to take a look at the websites of organizations like Freedom House that provide information about political freedom, freedom of the press, the rule of law, and other factors that may affect the business climate in a country.