I might be able to add a little bit into this thread from the aspect of the business' that do not seem to want to backup (or worry with the possibility). A major part of it is financial. Not always, and not necessarily the only reason, but often it is financial. That, combined with a general lack of understanding of the technical process or problems contained therein, is what often prevents a lot of business' from worrying about (or even thinking about) backing up data.
These companies (often smaller) are concerned with keeping their business going. They see the computer/technology as the method by which everyone else is keeping things going, so they want to make sure they don't fall behind. They often want to have the best and the newest and the fastest with the least amount of cost/trouble (heck, doesn't everyone?). Worrying about things that may or may not happen to cause them problems in the future may be a smaller concern to whatever other issues they may be facing at the given moment.
Our responsibility is to give them our best and make sure that they are functioning with as little trouble as possible. At the same time, especially in today's litigation happy world, we want to make sure that we are protected should any problems occur. And with technology (as many of us can attest to), it can be remarkably easy to inadvertantly have a problem. Explaining this to a business owner, especially a non-technical one, can be very trying. The owner may not care, may not have the money to do anything about it even if they do care, may have other pressing matters that may take precedence over "possible future problems", may put it off and forget about it, etc.
If a business owner has to make a choice over whether to backup existing data or make investments that will possibly increase their revenue, they are more likely going to make the latter choice in spite of the possibilities as far as their data goes. The same applies if they are in a financial bind, technology related resources are going to be much later on the list of things to worry about. It may not make sense to us on the technical side, but we have to remember it is we who are serving the business side, not the business side who is serving us.
That said, the best we can do, as several people have pointed out here, is to impress upon them the necessity of backing up data, and often doing a financial breakdown of what could happen if they don't is the most effective, keep our own notes and then do the best job we can under the circumstances we're allowed to work within as defined by the business owner. I have found that being flexible within these parameters is often the best that I can do. The other note I would add is, if you want to prevent the problems (since you are external), put the conditions into your contract under which you will work. Insanity is merely a state of mind while crazy people have a mind of their own.