The answer is YES! for Condo's and apartment. A definite NO for any land title deed. You can read more about the laws in Thaivisa.com.
I owned a condo unit in Chiangmai and I bought it in 2005 and I have rented it out ever since. Here's a simple guide (my own experience) on what documents and steps you need to do in order to complete the process.
Firstly, shop and look around for the unit you want and ask for a price. Even if the price is right for you, you could still try your luck and bargain a bit for a better price. Do note that you need to pay a transfer/purchase tax (20% IIRC)for the unit.
Open a bank savings account in the city you wish to purchase, its ok if you already have a account in another state but the inter-state transfer fees would be a pain in the ass. So just go ahead and open one in a bank near your soon to be condo. This also helps as if you plan to rent out and could ask the management to bank in the rentals to your bank easily.
The next step you need to do is either return back to SG or ask someone to do it for you on your behalf. Have a photo-copy of your bank passbook or the original and go to the Bangkok bank branch in Shenton Way and make a transfer to your newly opened account in SGD (not BAHT). If your bank is not Bangkok bank, you may need to pay an extra transfer fee. So I highly recommend you open an Bangkok Bank account to reduce these fees. DON'T go to Golden Mile complex or Western Union to do the transfer as its consider local investment capital, not foreign (that's why I say the transfer in SGD not BAHT). The next step is crucial, ask the teller to put on the receipt the reason for transfer is "For Purchase of Condominium" and nothing else. This is very very important as this document is required for translation and endorsement by the bank and Amphur (local state office). If you do not have this document. The officers at the Amphur have the rights to reject your purchase as they have no proof of where this money come from. Bring this or courier this original document back to Thailand and go to the bank you placed your money in. Show the teller and inform her that the cash is going to be used for purchase of condo and ask her to translate and endorse both the original and the translated copy. You can also at the meantime, use that money to purchase a cashier order for the real payment for your condo. Approach the seller with these documents and both of you will go to the local Amphur to transfer the name. The seller needs to provide the Chanande (title deed) and his identifications. At the amphur, show the officer the required documents and he will need you to sign some transfer documents (3 sets) and you need to pay the transfer tax. (Before hand, you should check with the seller if its ok to split this tax 50-50. If not, you may need to bear the whole chunk.) Pay the tax at another counter and they will issue you a receipt. Then go back to the officer with the receipt and wait for the person in charge to sign the Chanade (land title deed) . After handing over the Chanade, check your name and passport number is correct. Then just hand the seller the cashier order or proceed to the bank to pay him. NEVER NEVER PAY FIRST OR IN FULL even if the seller insist he wants you to. Wait until you get the deed and check first before you pay.
And viola, you have your own property in Thailand!!
Hope this little guide helps...