Trains, buses and taxis enter Thailand from Malaysia at the western point of entry, Padang Besar, or either of two eastern crossings at Sungai Kolok and Tak Bai. There is also limited public transport via much less-frequented Betong, near the centre of the Thai-Malaysian border. The crossing at Sungai Kolok is scheduled to be replaced or superseded eventually by the new crossing at Tak Bai in Narathiwat Province, which shortens the road link between Thailand and Malaysia by at least 60 km. Tak Bai was opened in September 1987 and has a boat jetty and ferry dock for boat service across the Kolok River, as well as customs and immigration offices. So far both continue in full operation - it's hard to conceive of Sungai Kolok closing, since it has long been a significant shopping and entertainment destination for Malaysian tourists.
There is currently no land passage between Burma and Thailand (legally) and likewise Cambodia and Laos, although we can look for Laos to open in the near future at the Vientiane crossing.