This situation is definitely an exercise in balance.

My preferred method is to just put an encrypted digital copy (CD-R, DVD±R, or flash memory) into the bug-out bag. This ensures that I have access to my documents if I have to bug out immediately (as in, no extra few minutes to grab the hard copies out of the file cabinet) as long as I can access a computer.

If I do have an extra few minutes, I will grab the hard copies and put them in the vehicle.

As far as the hospital situation that OldBaldGuy referred, I like MedicAlert’s approach. They give you a tag with an identification number on it instead of your name and info. Seems like a good system that prevents people from stealing your information by stealing the tag while also allowing the information to be updated as time goes by.