pros and cons...
Leave it on
No start up time
Pro - this is where most problems occur, similar to cold engines in cars-most wear then.
Con increases time running, so in theory will die sooner, but in practice 3-5 years is reached no problems most components, and anyway, your technology is ancient, so upgrade.
Components are maintained with some residual power
Pro - this is what they are designed to work in, so are warm and thus happy.
Con same as above.
No boot time-for Windows users with lots of programs and apps
Pro - big bonus.
Con programs can get themselves into a bind if left on, but a warm boot every day will clean this up-good reason for a coffee too! Windows users will warm boot often anyway, so no problem.
Leave it off
Sucks in atmospheric grunge.
Con - check situation if on floor and intake is low, best to either cover with washable foam or move to higher position.
Butdust is not necessarily the killer people think. I have seen dust on boards at yearly PM time in crappy situations, and the computers are happy they only then die when I power down, clean and boot up! Go figure!
Air conditioning turned off
Pro heat will kill the computer. Computers hate extremes in temperature, especially power supplies. Turn it off in this situation.
Is open longer to malicious attempts to compromise
Pro yes this is not good, but
Con forces you to harden the computer, which you should be doing anyway! Firewall-XP SP2 or ZoneAlarm, etc, Linux server @ $5 on old computer, etc, no excuse, just do it!
If storm comes and power supply goes nuts, machine may suffer.
Pro if off, it is still not 100%, but better than running and unprotected.
Con at the very least, get a power filter. If you are smart, you will get one fitted to the incoming power supply at the office/house and enjoy the benefits of all your technology being protected. BTW some insurance companies will give you a rebate of your insurance knowing your power supply is protected-ask. Also, get a UPS if computer data is critical.
Users as a rule should not have to open the computer unless they need to do something particular. As for cleaning and checking, leave it to professionals if aint broken, dont fix it. You only increase the chances of stuffing things up when you open, dust, fiddle, move cables, etc Leave it alone!
As a tech and user since 1986, leave the computer on in an air conditioned/stable temperature environment, and protect with filter and UPS, also Linux OS server/firewall, warm boot every day, speak nicely to them (I am not joking here!), replace bits as they die-upgrade time! Just check every now and then for dead fans, clean intakes, etc