Trying to summarize lots of information:
AS of today Saturday 21 March 2020 at 12:00:
Land borders with Thailand:
Malaysia closed their borders
Myanmar closed their borders
Laos closed their borders
Cambodia has a few border check points open today, but it seems from tomorrow onward only Poi Pet - Aranyaprathet border check point will be open for essential travel.
Thailand is closing borders as you can not travel to neighbor country anyway, no need to stay in full force to tell people, no border run available.
If you like to enter Thailand by airplane starting at midnight today, so effective from 22 March 2020,
all people need a medical certificate and an
insurance with at least 100.000 USD coverage.
Royal Thai Police Immigration Bureau:
Announced that for the 18 countries and 3 territories, the 15 day Visa on Arrival is cancelled,
The 30 day Visa Exempt Entry is cancelled for Italy and South-Korea.
There is an option for people using the Visa Exempt Entry and Tourist Visa and already have the 30 day Extension of Stay.
If you booked a flight out of Thailand before your last date and this flight is cancelled or re-scheduled or re-booked after your last date you can get an Emergency travel letter from your Embassy. With this letter you can get an extra maximum 30 day Extension of Stay.
For people using the Non Immigrant Visa, the normal requirements are in place to apply for the 1 year Extension of Stay.