I often see questions asking whether it's really better to leave a computer running all the time, or turn them off. The answer is, “it depends.” There's several factors involved:
Being connected to the mains, whether the computer is running or shut down, leaves it susceptible to receive damage from mains spikes and surges. Shutting the computer down doesn't really turn it off, it's still partially on. You need to switch it off at a mechanical switch, somewhere (e.g. the wall socket).
Electronic failure is more likely at turn on, than when a device is already running. There's a sudden increase in current at turn on time, this stresses components more than their usual operating conditions.
Electronic components do have a limited life, though it's a very long one, and they still deteriorate even if not used. But they're likely to outlast how long you want to own the computer for.
Motors have limited running life, and will eventually wear out (disk drive motors, cooling fan motors).
You have to wait for a computer to finish starting up before you can use it.
After running various personal computers over several years, with some of them left on all the time, some most of the time, some only as used, I've come to the following conclusions:
Monitors seem to be quite self destructive, and do sometimes catch fire. Dying computers will usually simply fail. You don't need to keep the monitor turned on, even if you do want a computer running all the time.
Cooling fans may last only a year or two if left running all the time. They start getting rattly after a while, then the chance of them seizing becomes greater. The tiny fans on graphics cards seem to be the worst. If a fan seizes, the device that they cool can easily, and very quickly, cook itself, causing crashes and permanent damage (power supplies, processors, graphics cards). Also, the entire computer can overheat if the power supply fan fails, as most power supply fans also act as the exhaust fan for the whole box.
Cooling fans do last much longer when the computers are turned off most of the time. They'll probably last for as long as you want to keep using that computer.
Computers are much more reliable with adequate cooling. Being warm isn't much of a problem, but being hot is. Once overheated, permanent damage can occur.
Hard disk drives seem to have the same life span either way. They have a limited running time, and a limited start-up life. There may be a bias one way or the other, depending on the particular drives, but I don't think it's very big one. Keeping them cool seems more help than anything else, warm seems fine, but some run painfully hot. They become unreliable in this condition.
The noise of the drives and fans drives you bonkers.
Your power bills will be lower if you shut them down when not needed, and they'll be even lower if you really turn the power off. This is more noticeable when you have more than one computer, and the same applies to other appliances which don't really turn off (remote controlled televisions, stereo systems, video recorders, etc.). Individually, the saving isn't very significant, but collectively it is.