As per Bank of Thailand rules, a foreigner needs a valid Thailand work permit in order to open a bank account. Opening a bank account is a straight forward process and takes about five minutes. All you need is your original Passport and Thailand work permit. There are scores of banks to choose from.
Normally, you would get a passbook, international debit card and internet banking facility with your regular savings bank account.
The ATMs of all banks are interconnected. You can use your Thai ATM card at any bank ATM in Thailand. However, a fee of 3 THB/transaction is levied after 3 transactions/month.
It might be possible to open a bank account even if you don't have a Thai work permit. Application of rules vary from branch to branch and are at the discretion of the bank manager. Generally, Kasikorn Bank and Bangkok Bank Branches at major locations in Bangkok are considered foreigner friendly. If you are refused by one branch, just try your luck at the next one. You might get lucky :)