One of the most popular shopping malls for tourists in Bangkok is MBK in the Siam Square area. Unlike other malls, this has hundreds of small shops where you can bargain the prices down. On the 6th floor in Zone B, there is a free bag deposit which is useful for people who have already checked out of their hotel and want to do some last minute shopping. It is open daily from 11 a.m. to 9 p.m. It is important that you pick up your bag the same day. You cannot leave them overnight.
If you know of any other free or convenient bag deposits in Bangkok then please mention them in the comments.