When Carrie and I travel we put all our electronic copies of our travel documents in the cloud. We use Dropbox for this. We can recall this from our smartphone, tablet, or our laptops.
Airlines provide all the documents as emails or pdf’s. Even boarding passes get send to you as an email. Showing a boarding pass as barcode on your smart phone to the security people at the airport tickles my inner geek pink.
As a precaution I still print out all my paperwork. I put it all together and have it ready just in case the cloud is not available. This gives the worry wart in me piece of mind.