If your computer is stable you can leave it on as long as you like. I know people that leave theirs on all
A normal, stable computer will not
get tired, it will not
burn wires, and it will not
effect the OS. The only thing that takes its toll are thermal cycles, tuning it on and off, about the only downside is that running all the time will increase your electric bill.
As for shortening the life span of the hdd as one of you implied, the hdd will not work any more than it usually will. As also previously posted, the computer hibernates when it has been left on its own, and unless there is an update which you have allowed (this is assuming that you have configured your firewall properly) will stay that way, the only things that will maintain running will be the spinning of the hdd, and what ever fans are not controlled or needed. It actually is the reverse here as far as the hdd goes, the spin-up and spin-down cycles are what are the hardest on the hdd, especially when spinning up cold. The hdd is a little motor, and like all single phase motors it has to reach auto-rotation, and until this happens there is a strain on that motor.
If you are concerned about burning carbon based fuels, I would suggest that you start looking at all the TVs, stereos, microwaves, basically anything that has an LED or LCD display that stays on. All of these stay on so that the start up time will be fractions of what a cold start would take, and they add up!
Having said all this, things happen, your computer could be perfectly fine only to have it develop a problem. This could happen whether you are there to witness it, or while you're away from the computer just to get a cup of coffee. One of your RAM modules could decide to die, or the PSU could develop a bad rail, or what ever...things happen whether you are watching them or not, and they are not usually catastrophic is such a manner as to endanger you or your house.
One last point here, google is your friend, use it, ask questions and learn, from some of the post that I've read here I'm almost surprised not to have heard suggestions of sacrifices in the light of a full moon, a CPU ripped from the case of a live tower!