Why save images to the cloud? Because if my bag gets stolen, my smartphone is also going to be gone, so I need to be able to access my information from a public computer anywhere, anytime. I now take three VERY high quality images of the following and save them to the cloud for emergency backup before boarding onto a plane:
1. Primary passport pages: These are the pages with my photo, home address, and passport number. Having your passport number will speed up the process at the United States Embassy if the original is stolen, lost, or needs to be replaced. The alternative is to get a passport card, which has this same number on it (my friend had hers in her wallet, so that was lost too).
2. Credit card: Many hotels won't allow check-in without the credit card the reservation is associated with. While some hotels might be more lenient in the case of a stolen card, it's helpful to be able to source the numbers should this situation arise.
3. Prescription information: Many travelers carry their medications in their purses or backpacks for ease of access while visiting tourist spots, but don't think about the consequences of situations when access to those meds is limited or blocked. Many pharmacies in highly traveled areas (think London and Paris) will be able to fill pretty standard prescriptions if they have access to appropriate information and don't mind calling the States to confirm the prescription with a doctor or pharmacist.
On past trips, I've also taken high quality images of my bags, just in case they turn up misdirected at a hotel or airport, so staff can quickly and easily identify them and return them to me.
(Photo Credits: Tiffini and CarbonNYC via Flickr's Creative Commons)