If you were running any other OS than Linux, I'd start off with the hardware suggestions.
However, my experience with Linux is that unless you're working with marginal hardware drivers, it's not that likely to just go down. The closest I've gotten in the last 2 years is when I get too many Netscape windows running and the Virtual Memory starts thrashing to the point that it's faster to reboot than to wait for the churning to stop. Netscape may die, X Windows may die, but Linux itself is likely to still be running.
So the first thing to do is figure out what's killing the system. If only the outer layers are dying off, you can often telnet (ssh recommended) in and clean up the dead processes. Ideally,
you should find what's killing those processes and fix them, if possible.
However, if the system is well and truly crashed to the point that neither Internet nor modem dial-in access can get control, you're probably going to have to do a hardware reset. Depending on the machine, you might be able to wire something to the reset button (if it has one). Otherwise you'll have to interrupt power.
One simple and fairly inexpensive way to do this is via home automation equipment such as the X10 series (when not running cheesy adverts, they actually DO produce useful products!). For example, there are units that plug into the telephone that will send a signal over the building's power mains to where a receiving
unit can be used to switch power off, then on. I've bought other units as well - one could actually be wired to a reset switch - it's a low-voltage switch designed for controlling sprinklers, landscape lighting and the like.
The downside to this is that anyone who knows that you have this kind of equipment set up could dial in and reset your system! It has very little in the way of security.