Visas rules keep on changing as the relations improve or deteriorate between countries. Here is a list of countries of continent Asia for which American citizens need a visa . Also the countries where the American citizens will not need a prior visa are mentioned here . For the countries where Americans need a visa to enter they will need to apply for a tourist visa or other type of visa in the Embassy or consulate of that Asian country. You can find list of Embassies in United states of America of that particular country and call them for more info regarding the type of visa you need. Some countries as we have mentioned above will give American citizens a visa when the US citizens will arrive at their airport or point of entry. However for the other countries a US citizen will not need a visa to enter. This sort of entry is called a visa waiver. Since the security have been raised in almost all of the world after Sept 11 incidents A US passport is required for almost all of countries where a American National will need to go. If the visa you are applying is a special sort of visa like a work visa or permanent resident visa of that Asian country you are going to than you can hire Experienced immigration attorney or lawyer who will assist you to fill up the forms and can guide you of the process. The sources used to collect this data is Wikipedia and embassy websites of the countries.

Countries and Territories Conditions for countries
Afghanistan visa for Americans(US citizens) For a visit to Afghanistan for tourism or business Americans need to apply for visa in advance.
Bangladesh visa for Americans(US citizens) Bangladesh offers 90 days visa to US citizens upon arrival.
Bhutan visa for Americans(US citizens) American need to get visa prior to their arrival in Bhutan.
Brunei Darussalam visa for Americans(US citizens) Brunei Darussalam is Visa free for US citizens if stay is less than 90 days.
Cambodia visa for Americans(US citizens) 30 day visa issued upon arrival to Cambodia for American passport holders.
China visa for Americans(US citizens) irrespective of American citizen purpose of travel to China (PRC) the US citizen will need to apply in advance for a Chinese visa to consulate or China high commission near you. China has multiple consulates in USA.
Hong Kong visa for US Citizens (US citizens) Hong Kong offers a visa free travel upto 90 days for American people.
India visa for Americans(US citizens) American nationals need to apply for a visa in advance for India for a fee to one of its consulates in USA. American citizens can apply for a visa in Indian embassy in Washington DC. Other Indian consulates in USA are in Chicago, New York, San Francisco and Houston.
Indonesia visa for American Nationals (US citizens) For American people Indonesia offers 30-day visa issued upon arrival.
Japan visa for Americans(US citizens) 90 days visa free travel for American traveling to Japan for tourism or business purposes.
Kyrgyzstan visa for Americans(US citizens) 30 day visa is issues by Kyrgyzstan on arrival to United States of American Citizens.
Laos visa for Americans(US citizens) 30 day visa is issues by Laos on arrival to US citizens.
Macau visa for Americans(US citizens) 30 days visa free to Macau for American passport holders.
Malaysia visa for Americans(US citizens) American citizens donot need a visa for Malaysia if their stay there is less than 90 days.
Maldives visa for Americans(US citizens) American citizens are offered 30 days visa free entry to the Maldives. If your intend to stay beyond 30 days than you need to apply for a visa before your arrival.
Mongolia visa for Americans(US citizens) Mongolia offers 90 days visa free for US citizens
Nepal visa for Americans(US citizens) Nepal offer a visa on arrival to Americans
North Korea visa for Americans(US citizens) Due to tensions between two countries there are special travel requirement for the US citizens who want to go to North Korea
Pakistan visa for Americans(US citizens) American citizens need to apply in Advance if they want to visit Pakistan
Philippines visa for Americans(US citizens) 21 days visa free to Philippines for US citizens who want to visit Philippines
Singapore visa for Americans(US citizens) US citizens will not need a visa to travel to Singapore if their stay is less than 90 days.
South Korea visa for Americans(US citizens) US citizens will not need a visa to travel to South Korea if their stay is less than 90 days.
Sri Lanka visa for Americans(US citizens) US citizens and passport holders will not need a visa to go to Sri Lanka if their intention to stay is less than 30 days.
Taiwan visa for Americans(US citizens) US citizens will not need a visa to travel to Taiwan if their stay is less than 30 days.
Thailand visa for Americans(US citizens) US citizens will not need a visa to travel to Thailand if their stay is less than 30 days.
Timor-Leste visa for Americans(US citizens) 30 day visa issued upon arrival for US$30
Turkmenistan visa for Americans(US citizens) must apply for a visa in advance if your want to visit Turkmenistan
Vietnam visa for Americans(US citizens) must apply for a visa in advance to Vietnam but the visa can be collected at the airport once the US citizen arrive to Vietnam

We have tried our best that this list is updated and correct however it is advised to double check. The most accurate information in this regard can be collected from the embassy of that particular Asian country. Some times the airlines you will be taking for your travel can also provide guidance on the visa requirements.