For me, it's a money belt at all times with deep storage items like passport, debit and credit cards, copies of phone numbers/acct. numbers in case of theft, etc, all in ziplock bag to keep everything nice and dry. AND I carry an across the body small lightweight purse with compartment for small amt of money, small digital camera and one day's extra batteries, lipstick/chapstick, tissue, etc.
My husband wears an Eagle Creek hidden pocket (http://www.letravelstore.com/4002410_048.html) and carries an RS Civita Day bag with umbrella, water bottle, bandana (multiple uses), pages from RS books, maps, etc.
As similarly stated by others, I have too much to see and too many things to do to worry with having to replace a passport or cancel credit cards. Very often you are not on guard against problems and pickpockets because you are too busy being a tourist and oohing and aahing over things you see and experience. It's very obvious that you are a tourist, and although chances are nothing will happen, I'm not willing to take that chance. Generally we have stayed in less expensive hotels that do not have room safes. And I have read too many horror stories; my travel time and dollars are too valuable to waste. Once I read on the helpline that an American passport is a really hot item on the black market....nope, I'll keep it secure and hidden.