Here is the relevant link from the
Royal Thai Embassy- Washington, D.C. "Tourist Visa Exemption"
(The link posted up-thread is not a genuine government site.)
http://www.thaiembdc.us/dcdp/?q=Tourist_Visa_Exempt
Relevant details:
Travelers Advisory:-
Due to the requirement of the airlines in the United States to the travelers, it is advised as follows:
For the US passport holders and other countries, which are in the tourist visa exemption list, they are advised to confirm the return airline tickets within 30 days, both arrival in and departure to Thailand.
If the duration of arrival in and departure to Thailand on your confirmed return airline tickets is more than 30 days even though you plan to stay in Thailand not more than 30 days, you need to apply for a tourist visa.
Please allow yourself at least 10 days before departure date to apply the tourist visa, in person or by mail, at your nearest Thai Embassy, Thai Consulates-General in Los Angeles, Chicago, New York or Honorary Consulates- General (Honorary)