Yes. Holders of U.S. (American) passports may currently travel to 186 countries without having to obtain a visa in advance of travel. These countries allow either visa-free entry or issue visas on arrival.
But, a U.S. passport does not guarantee entry to any country. Each country’s border control is still free to decide whether or not to allow entry to a particular individual.
Travel to some countries, or regions is also restricted beyond the typical need for a visa. For example:
North Korea. To travel to North Korea one must have special validation from the U.S. Department of state- North Korea International Travel.
Cuba. Travel to Cuba requires special authorization – Cuba International Travel.
Mecca. U.S. citizens who are not Muslim are not allowed to visit Mecca and certain parts