There is a similar question on Server Fault that addresses this. Mark Henderson raises some very valid points and makes an excellent analogy about cars:
To liken it to a car analogy: A taxi can do over 500,000 kilometers before it needs an engine rebuild. The reason for this is because they are always running, 24/7, and after a car's engine is up to temperature, the amount of wear it receives while it is running is greatly reduced.
He is 100% spot on. Think about it, when your computer is sitting idly what is it doing? Not much: answering broadcasts over the network, maybe some background programs are phoning home or checking to make sure they are up to date, but generally (unless you have a virus) nothing. In modern systems the CPU throttles down, the Hard disks spin down, the display output is shut off so the video card isn't rendering.
Now think about when you start up: all your components (CPU, Hardisk, Motherboard, graphics card, fans) all start drawing full power and this puts an abnormal amount of stress on the power supply and the drives (which are going from a cold state to 5400/7200/10k RPMS). From Wikipedia:
Shutting down and rebooting a computer or resuming it from hibernation cycles the power to the drives in the computer. The spin-up operation performed by a drive after a power cycle is believed to place more stress on the drive than running the drive continuously for a long period of time.
Based on professional experience of system administrators, it is believed that there is a direct relationship between the number of power cycles of a computer and the probability of failure of its drives. In other words, a computer with a high uptime may have a lower probability of drive failure than one that has its power cycled routinely.
To add some personal experience to this, my desktop PC was built in 06 to this day I have never turned it off (other than a warm reboot or the odd power failure) I have also not had a hard drive die in it yet (it has 6). Just in my current laptop I have been through 2 hard drives already, I boot when I get to work in the morning, boot up again after dinner, and then maybe one more time before bed. I could also mention similar experiences with the servers and SAND's (storage attached network devices) but since enterprise and consumer hardware are a bit different I'll leave it out.
As far as your side question about hibernation and sleep: When you hibernate the computer saves a copy of your pc's current state to disk and stops drawling power entirely so it is basically like shutting down. The disks will have to spin up and the computer will draw power like it was cold booting, it will just load the hibernation file and when it is done booting your computer will be in the same place you left it when you hibernated. Sleep however may be a little better since it will continue to keep your PC's current state in volatile memory (meaning memory that needs power to function) so it will still draw a small amount of power, but your hard drive won't have to work as hard when it is woken up again which is a benefit. For more info see this article from Microsoft
let it run 24/7, you might get different results topower on/off over nightor5 times a day. I would expect different components to react differently. The fan is more polluted by constantly running, I guess, and not so much impressed by turning on and off. Other components might suffer more from changing temperatures. – user unknown Apr 13 '11 at 3:21