Always. In addition to everything everyone above has said, there is also the 'appearance' factor'. I have watched other people, including colleagues, be grilled about their plans by immigration, and having to bring up info on their phones, dig around in bags for scraps of paper etc. I've come to realize that you are often treated better (airline, immigration, hotels) if you are organized - for complex itineraries I carry everything in a folder, information in chronological order, tabbed according to whether it is a flight, hotel, car rental, visa or other document. Having print outs has saved me a few times, especially when hotels have tried to tell me my reservation is not paid (when it was a pre-pay), that I did not reserve a non-smoking / king bed / club room when I did, and being able to get from an airport to a hotel in a country where I did not speak the language, nor did the driver, but the picture of the hotel on the print out made him say 'ah ha', and took me to the right place!