Plain and simple - old hardware tend to die at some point. Add a Murphy's law to that, it will die when you least expect and desire it to happen.
A death of experimental web development server will probably only cost you a small disappointment (yeah, and I do hope you backed your code up), while a file server with the family movie collection can really be upsetting.
The best way of dealing with that is firstly to decide how critical this machine will be. If its a file server, make sure to have new hard disks for it (and make a backup!).
If its a firewall machine, keep another one like that in case of a major failure.
I actually came across the situation whenever old machines were used as a firewalls, and every time they failed, it caused a major disaster with the few hours downtime for the whole business (home business I should add, so it wasn't that bad).
The components you really should look out for are
- Hard disks. Normally they live for 3 years, no more. (yeah yeah, I know, you probably have one that lived for 12, but not if the machine is constantly on). Therefore 3 years is what you can rely on, after - you're on your own.
- PSUs. They break a lot. Especially the cheap ones. Especially if the computer is not on UPS. Especially if you don't even have surge protected power board. Especially in the countries like Australia, where you have power surges every summer, quite a few times.
- RAM. They used to break a lot in the old machines, for newer machines its no longer the case. In fact most of the new RAM you buy these days comes with the lifetime warranty.
For old machines its still the case so beware.



