Tourist visas are not required for Americans traveling to Canada or Mexico. This is true for all U.S. citizens and permanent residents. All that is needed to travel to Canada or Mexico is a passport or enhanced driver's license.
A general rule to follow when questioning whether a nation requires a tourist visa of Americans is whether or not their citizens are required to obtain a U.S. visa for travel. Many nations require visas of any nation that requires visas of them; this is known as reciprocity. This policy is taken by a great many nations against the United States as a political statement. Examples include Turkey and Brazil, who immediately after being required to obtain U.S. visas began requiring U.S. citizens visas for tourism.
The Schengen Agreement made European travel and visa queries simple for Americans; all member states of the agreement (members of the European Union) do not require visas for U.S. citizens to enter as tourists. This means all EU members can be visited by U.S. citizens without a visa. There are certain nationalities, however, that are required to obtain a Schengen visa to travel through the area.
Though it is crucial to look up the visa policies of every nation individually at the U.S. Department of State website (travel.state.gov), there are certain regions that you can predict will require a tourist visa. These include most of Eastern Europe, the Middle East, Africa and Asia. Parts of South and Central America require tourist visas, though not all.
A few of the most visited countries (by Americans) that require a visa include Russia, Brazil, China, India, Bolivia, Turkey, Vietnam and Greece.
