Back in the days before the public became aware of the internet [i.e. before the WWW] I ran a BBS on an original IBM PC - 24/7 for two years. I shut it down after two years for some reason I don't recall anymore, and, after a couple of weeks being off, when I went to restart it; I got POST errors out the wazoo. In effect; it was dead. The reason? The curcuits cooled down too fast and probably created some hairline fractures in the pathways.
So keepiing it on and running for so long could create a similar type problem although today's computers are probably more thermally tolorant in some areas. Now both AMD and Intel HighSpeed (> 1GHz) processor's today do run hot. They all run with cooling fans attached to the heat sinks. If that fan fails, you have about 1~3 seconds before processor meltdown. That senario is offset with newer BIOS' and motherboards with thermal & fan sensors that can shutdown the system if it senses failure in those components or a rise in temperature.
If you are connected to the Net via Cable/DSL "always on" connection, then you had better be running a firewall such as ZoneAlarm. I myself run with ZoneAlarm and I also have a Firewall/Router/Hub that connects to my cable modem. LinkSys sells one for about $99.00. If you don't have such protection then you should shutdown at night.
Power: A UPS is a must. As mentioned by others there are energy considerations. Newer motherboards will allow Windoze power managment to idle the processor, harddrives and network adapters when unused for a preset length of time. It's you call on that.
As for the strain on components of starting up? Harddrives would be the most suseptable component for such trouble as it has the most moving parts and heating and cooling would take its toll. Fans will generally start to let you know of impending failure with the sound of their bearing(s) going out. I've never seen one just up and stop on its own without such warnings. Though I have seen some not want to spin up after a system was shutdown and they cooled a bit.
If you do decide to run your system 24/7, make sure it's in a cool place, out of direct sunlight and has plenty of ventilation.