There are quite a few arguments for and against running a computer 24/7.
First of all - electrical components only have a certain operating life - naturally if it's used less, it generally lasts longer.
The same is true with hard disks - mainly due to the moving parts, they only have a certain number of running hours.
This is probably the first point of failure in a constantly running system.
However, the reverse is also true; HDD's only have so many 'stop-starts' - the strain the motor is under while spinning up the drive lessens it's operating life.
In cases such as high-end server disks, the drive is much more likely to fail if the machine is shut down every night, as opposed to the drives remaining running constantly. Im not sure how the new IDE drives around nowadays behave with regard to this.
Heat is always an issue. Most Hard disks dont generate much heat (in comparison to say, a half-height 6-platter 7200rpm barracuda), but in an enclosed environment over many days, small sources of heat tend to increase exponentially, so make sure you have adequate case ventilation and component cooling.
For Instance, the I960 chip on my raid controller gets a bit warm, but not too hot, yet over a few days it will increase the case temperature by about 6 degrees... no doubt it would keep rising, too - so a 486 HSF fixed that problem.
I dont know if the Northbridge on your mainboard is cooled, either directly or indirectly, but thats another one to watch out for.
Overclockers - even the oscillators which are part of the integrated VRM which provides current to the CPU get very warm when you run a CPU over it's voltage spec. It's always good to try and cool the things.
I am still of the belief that it's not only more economical, but also more practical, and certainly NOT detrimental, to have your machine running 24/7.
And in SCSI systems, if you ever suspend your PC - leave the disks running - they'll last longer 😉