Savings Accounts by nature don't fetch attractive interest rates, however the General Impression that I have had is that Commercial Bank of Qatar is the best private bank in Qatar. With respect to the interest rate on a Savings Account with this bank, I get 1.50% p.a. (per annum), which is as stated above very minimal.
They usually have excellent offers on hand as well, the last time I remember customers were given iPods and other valuable gifts for just opening accounts there and transferring one's salary. As simple as that!