Can Linux Work Without Shutdown?

Glen Raphael submitted this odd question a while ago: "Suppose I have a test tool running under Linux in an environment where the power is expected to die often and for long periods of time without any warning (and buying a UPS isn't an option). How can I make it safe to just turn off the power to the PC running Linux without properly shutting down?" So what is one to do when they want to run a Linux box and they can't trust their outlet? Glen continues...
"It's okay for fsck to run at startup but I want to minimize the damage it has to repair and I want to entirely avoid the need to boot as root in order to repair major damage. What can I do to accomplish that goal? Performance is not an issue. I thought of doing a "sync" every minute or so, but that seems silly. Is it possible to turn off disk caching instead and if so how do I do that? What else can or should I do in software to ensure that you can turn off the Linux machine by hitting the power switch or cutting power to the building and not expect major repairs when the power comes back up?

(Side note: If this problem can't be solved, the favored alternative is to give up on Linux and rewrite the tool using DOS. Right now I'm using RedHat 5.1 or 5.2 on a generic Pentium notebook.) "