I agree with edfair, flashmedia, drosendranz, and numerous others who have posted here.
I've been using PCs since the mid 70's, and have been building/supporting them since the early 80's. Probably the biggest cause of failure in PCs is heat. How can you minimize the heat that's generated? Shut the system down when you're not going to be using for some length of time, say 4-8 hours or more. Yes, there is a wear cost associated with booting a system, but there is also a wear cost associated with leaving a system on all the time.
In the early days of PCs, when a power supply was in the 63.5-135 watt range, the power spike to the power supply when booting up could indeed "fry" the PS, so many "knowledgeable" computer buffs determined that they should leave their systems on continuously to prevent the chance of this happening. Current systems, though, with power supplies in the 300-350 watt (and higher) range can absorb this without too much complaint. Other components are designed to better deal with the "trauma" of starting up. (Beware though, because many of today's low-cost systems offer power supplies in the 160-180 watt range, which is JUST enough to power the components designed into the system, without the addition of any other components (CD/R-RWs, DVDs, etc.), or to provide the "overhead" to be able to absorb a power spike.)
Similarly, old MFM hard drives originally had a MTBF (Mean Time Between Failures) of 10,000 hours or so, while IDE and SCSI hard drives now have a MTBF of 100,000-300,000 hours. If left running continuously, this would amount to 11-33 years. Why then do most hard drive manufacturers guarantee their products for only one year, or two, or three at the most? (A year is 8760 hours.)
If you DO choose to leave a PC running for extended periods of time, be sure to change the Power Management settings in the BIOS to power down the hard drive after some reasonably short period of time, 15-30 minutes, say, because if the system needs to access the drive, it'll spin it up again to read/write whatever it needs. Also, be sure to set your monitor to remove voltage from the guns (rather than just clearing the screen, as a screen blanker does). Most newer monitors have this capability built right into them.
Also, servers that are left powered up for weeks and months on end are usually in a temperature-controlled environment. Is your home or office maintained at a constant 68 (or lower) degrees, with emergency procedures in place if the temperature rises above this?
The most commonly replaced component in PCs (in my experience) is the modem. And a modem failure is most likely caused by a lightning strike somewhere in the vicinity (though not necessarily close). Every PC I build is delivered with a surge suppressor of at least 3000 joules. (A joule is the measure of "clamping power".) Many of the "surge suppressors" sold in computer stores or elsewhere offer 300-500 joules, which is better than no protection, but perhaps gives a false sense of security that a person's computer is protected. Be sure to get a surge suppressor that also has protection for a phone line as well as a TV cable, to prevent damage to the internal modem or the external cable/DSL modem.
Keeping computers running for over 20 years... (though not necessarily running continuously...)
Rich (in Minn.)