We feel extremely safe aboard the ship. We also have found it best not to tempt people needlessly. So anytime we are in an area where there are fellow passengers we maintain possession of our valuables such as electronics.
While cruising our jewelry, passports, drivers license, credit cards, etc. go into the stateroom safe along with any cash that is not needed for tips, just like many others. With the exception of my ever present iPhone, we also usually leave our electronics in our room.
Most often my wife and my sea pass cards on in my pocket. As many have pointed out, most women's clothes do not have pockets so I carry hers for her.