We recently produced a video about the Best Foreigner Friendly Banks in Thailand.
Based on reports from our subscribers and general reviews, Bangkok Bank seems to be the most foreigner friendly bank.
However to open an account at the bank, its best to do so in areas of Bangkok that has a lot of foreigners. This ensures that the staff in that location understands the needs of foreigners.
It's one of the few banks that will open an account for tourists with an affidavit letter from their embassy and identification.