Keep your most important travel documents in the cloud. That means either emailing yourself copies or creating a file on Google Drive or Dropbox you can easily access. Important documents include your passport, your driver's license, and your hotel and other confirmations. Even consider having a copy of your birth certificate.
I once had my passport stolen in Prague but was able to get a temporary one at the US consulate quickly because I had a copy of all my documents, including my birth certificate. Today you don't even need a scanner or copy machine to make duplicates — just snap a photo with your phone. Be sure to get both the front and back, when applicable.