There are different types of travel visas, but tourist and business visas are most common. Most countries do not require a tourist visa prior to your trip. You just fill out a visa card on the plane or at your arrival airport.
Normally there is no fee, but some countries may charge you a small travel visa fee at the airport.
It is good to carry a couple of passport pictures when you travel to certain Asian countries just in case.
Western European countries (or those that belong to the European Community) do not require any visa for USA citizens.
Latin American countries such as Brazil and Argentina do require a visa for USA citizens.