A friend who worked in the State Department recommends scanning your passport and the front and back of any other documents or id cards you may carry with you (driver's license, health card, credit card) and attaching them to an email to an account you can access (such as gmail or hotmail).
I put about eight id/credit cards on the copier, scan them, flip them all over, and then send them to myself in an email with a subject line like "Cutest puppy pictures ever" or "Mom's b-day party pics". I figure that hackers are scanning for emails with subject lines like "Copy of Credit Cards" or "Important documents"
I've got a traveling companion that has needed to go on the Internet and pull up those pdf files when their wallet was stolen. The scans had the credit card numbers as well as the credit card company contact phone numbers.