I used to run a pretty big farm of machines at home, and heat is the enemy as already pointed out.
However, there are other things that can and do go wrong, because you are running the system 24/7. These include wear and tear on moving parts. Fans tend to spin up more if they are regulated, because the CPU or GPU load is higher for a much higher percentage of the time.
Using a good quality CPU heatsink/fan combo is highly recommended.
General good practice like cleaning your rigs every quarter for PCs in a reasonably low dust environment is not a bad idea. For laptops, definitely clean the air intake/exhaust as much as you can without dismantling it, blow out the dust which it will gather a lot more than PCs in general (at least, that is the case for myself hehe)
Power supplies in cheaper systems or cases tend to be highly optimistic, stating 600W power when that is the maximum power at 25 degrees C. Even branded PSUs are usually rated at 25C, which is not a realistic temperature in a regular computer, most of the time case temperature is at least 40C. Check the continuous rating and make sure you stay well clear of it, say max 80% at worst-case load. If your PSU can easily handle the load whilst folding, it will run cooler, potentially less noisy if regulated fans are used, plus it will last a lot longer.
The biggest cost for me apart from electricity was PSU fans on the cheaper PSUs, or the caps blowing due to the heat inside the cases caused by insufficient cooling. The latter should not happen much these days as most manufacturers now use better caps, etc.
Hard drive wise, same thing, keep it cool. If you can throw a low speed 12cm fan in front of it to increase the airflow it will keep it cooler and will probably extend its life by a fairly significant amount.
Either way, with a little maintenance and thought about heat related issues in general, there is no problem