First of all, it cannot happen to me because I have all my important papers in a safety deposit box at the bank.
However, most important records have an original copy recorded with a public agency. Driver’s License, birth certificate, social security card, and most financial records are kept by the issuing agency or bank. Getting the new Driver’s License would probably be easiest, since all you have to know is your name. Getting a new birth certificate is very easy, I have gotten for all my family simply by calling the county recorder where the birth took place. (You have to send money). If you don’t remember your social security number, it might be a little harder, but your employer has to have it on file.
You surely know the name of your bank, so I can’t see where that would be a problem.They have a signature card on file, and can use that to verify your identity.