Owning a house is possible in Thailand, but only if you build it yourself, and submit lots of paperwork. You do not own the land on which the house is situated, though. Foreigners can not own land in Thailand. (Think: "ไผทของไทยทุกส่วน" from the national anthem - they really mean it!)
A company is a legal entity, and can own land - and there are two ways (that I know of) for a foreigner to own 100% of a company. One is for US citizens only, and the other is to start a BOI company. Both a little convoluted, but can be done. If the government suspects that the company only exists to allow a foreigner to control Thai land, they will close it down.
You can not own 49% of a piece of land, even if married to a Thai national. If married to a Thai and they acquire some land, you have to sign a document stating that you will not have anything to do with the land (go on - ask me how I know!).
OK, that's houses and land covered. Condos ... you can own one of those outright, but you have to prove that the money you use to buy it (outright - you can't get a bank loan to buy one) comes from overseas. The exclusion to this is if you have a work permit, where you do not have to prove that, as you are allowed to earn money in Thailand. There was once a case where you could get a bank loan for purchasing a condo, but it was from the SG overseas branch of Bangkok Bank, and the conditions were ... not favourable.
Also, foreign ownership of condo units in a building is capped at 49%, but that's only a problem if buying in an area with lots of other foreigners.
Finally, the most important thing to remember, is that foreigners can not own the tiniest piece of land in Thailand. There are no exclusions to this rule, and if you see someone claiming otherwise, they are trying to sell you something that you will not actually own.