The topic of visas for Americans is a tricky one. Many countries require no visa, some require a visa upon arrival, and a few others require obtaining a visa in advance. Countries like Aruba, Belgium, El Salvador, Finland, France, and Greece do not require a visa at all. The only thing noted is a maximum stay of 3 months.
There are other countries that allow varying stays of 30 days, 3 months, 4 months, 6 months, etc. Other countries including Oman, Nepal, Lebanon, Kuwait, Indonesia, and Ethiopia all require a visa upon arrival which is typically simple to obtain before leaving the airport. Finally, countries like Brazil and Russia have visa requirements that are relatively expensive and must be done several weeks before your trip.