Southeast Asia is generally open to US citizens, with different degrees of visa-free access throughout the region.
Most countries in Southeast Asia allow fairly easy visa-free entry, or visa upon arrival, for stays ranging from two weeks to three months. The only exception is Vietnam, which requires US passport holders to get prior visa approval at a Vietnamese Embassy or Consulate.
So if you're planning to hop from country to country in Southeast Asia, be sure you're prepared long beforehand with the proper requirements, so you don't hit a wall at the immigration gate.
US passport holders may obtain a visa on arrival; just provide $20 and a passport-size photo. Your visa will let you stay on for a maximum of one month. Cambodia also offers a slightly more expensive, but vastly more convenient, Cambodia e-Visa that you can apply for online. For more information on getting a Cambodia visa, read this article: Cambodia Travel Information
US passport holders may get a visa on arrival, with a fee that depends on how long you plan to stay (30 day maximum). For more information, read this article: Indonesia Travel Information
Visa on arrival for US passport holders may be purchased for $35; maximum 30 days' stay.
US passport holders visiting Malaysia need not get a visa if visiting for social, business or academic purposes. Visitors can stay, visa-free, for a maximum of three months. For more information, read this article: Malaysia Travel Information
US passport holders must obtain pre-approval for a visa from the nearest Myanmar embassy or mission. For more information, read this article: Myanmar Visa - Entry Requirements and How to Get Your Visa for Myanmar. More general information also available here: Myanmar Travel Information
US passport holders may enter without a visa, for stays not exceeding 21 days. Visa Extensions can be obtained from Philippine Embassies, Philippine Consulates, or from the Bureau of Immigration within the Philippines. For more information, read this article: Philippines Travel Information
US passport holders are not required to obtain a visa to visit Singapore; the Entry Pass permits a maximum stay 30 days. For more information, read this article: Singapore Travel Information
US passport holders can get a stamp on arrival, permitting them to stay for up to 30 days. A single 14-day extension may be obtained. For more information, read this article: Thailand Travel Information