The rule of thumb is anything mechanical, while in motion, will wear out. For a PC that mostly means HDDs and fans, but sometimes also floppy drives and even switches (so keyboards too) if used a lot.
Then there are tubes, and that includes CRTs - even if not displaying anything bright, the cathode, while heated, will loose emission over time. Obviously the screen phosphor itself can be burned out too.
Electrolytic capacitors are next, and their lifespan depends highly on temperature - not ambiet, internal. So either hight ambient temps or high current spikes will slowly dry it out. They also dry over time but way more slowly, modern ones will last many decades.
Everything else doesn't really wear out unless it's highly-stressed semiconductors. There's no rule for those, you can never know how close to safe margins they are, no point in worrying unless you have some reference datapoints (like, you know for a fact that certain chips, in certain systems, do die after X amount of time being powered).
So the next thing to worry about it transients and surge currents during power-on/off events. Those can be bad for early switching-mode PSUs, but also CRT monitors. That being said PSUs can be repaired or replaced and any CRTs still left are living on a borrowed time anyway. That is why it was recommended to not power-cycle PCs without reason, but lets not get too crazy - once/twice a day is what the equipment was designed to handle for years. Something is going to die, eventually, from use or disuse anyway.
And then there modern high-density Flash cells like in SSDs, that needs to be powered on at least once per few months, so that the controller can do proper housekeeping, find any weak cells and migrate the data before it's too unstable to be read out.
