When I moved to BKK last year, I think only Bangkok Bank had an option of opening a bank account for non-residents without a Work Permit (account and local access ATM card only, other services like internet banking require a work permit). All other banks required a work permit before opening an account. More info about the Bangkok Bank account can be found at:
http://www.bbl.co.th/Bangkok+Bank/Pe...rs/default.htm
http://www.bbl.co.th/Bangkok+Bank/Pe...+Questions.htm
If you have a work permit, I've been told its a breeze opening an account (at least compared to getting the work permit). That said, I've gone exactly 1 year as of today without having a local bank account even after getting my work permit.