This is a question we have had to answer for many years. As your OP recognizes, there are different levels of need.
The most common, and easiest, in my opinion is the travel situation. We've been able to provide a continuum of service while we travel/vacation through laptops that are running a mirror of all our business and client files. It takes some time each day to just check in on everything, but it has worked.
Getting hit by the bus or seriously ill? It scares me to think how vulnerable we are. I am looking forward to watching this discussion.