I like to always have printed copies in case the airport doesn't provide wifi (or my hotel doesn't give wifi access before check in). There's always a chance that the airline won't be able to find my reservation and ticket or that a hotel will lose my reservation, try to charge a different rate, or assign me a lower room category than what was booked. In the USA, of course my cell phone does the job to let me find confirmations and receipts in my email, but my equipment is not compatible with cell phone service in a few countries, nor is it always easy/convenient/cheap to get cellular coverage in all locations.