The visa on arrival as described on this website lists the entry points into Thailand. We have now listed the countries which get a visa waiver. This means that you can enter Thailand for 30 if you arrive via the airport and 15 days if you arrive via a border crossing.
Note that it is much better to apply for a tourist visa before you arrive in Thailand as this gives you more options with regards to your stay in Thailand. The visa on arrival or visa waiver has no extension options like a tourist visa would have. These are the countries who are allowed 30 days on arrival, 90 days on arrival and also 15 days on arrival. Note again that this is by entering Thailand via the airport and not a border crossing.
If you are planning on staying in Thailand for longer than 30 days then it is best to apply for a tourist visa or if you are going to enter Thailand via a land border then a tourist visa is also a much better option. If you are over the age of 50 then you can apply for a retirement visa or if you have Thai family then a marriage visa is a better option. If your country is not listed then you need to pay for the visa waiver which is 1,000 Baht and you need to show that you have a minimum of 10,000 THB on you when you arrive.