Modern computers usually go into 'standby' mode after a set time of inactivity, which puts all the circuits into idle, and doesn;t use as much electricity to re-commence as a full-scale boot-up.
In terms of harming the computer, i would say the dame is negligable - some say you do more harm powering up and down for short periods than you do by leaving your PC on all the time.
As andy says, it won't really harm it. For the CPU, it's more damaging to be constantly heating it up and then letting it cool down.
It's more that it'll be using electricity as llamatron says, unless you put it to sleep.
If the computer is being rarely restarted though, then you have a memory management issue. Some OSes are good at dealing with this (the UNIX variants basically); Windows isn't as good. You'll want to restart every few days anyway.
according to this https://www.cia.gov/cia/publications/factbook/print/uk.html
, in the UK, most of the electicity that you waste by leaving your computer on comes from burning fossil fuels, therefore it contributes to global warming.
So no, it is not OK to leave the computer on, even if you don't pay the bill today, you will pay for the consequences later.
In my last job, I supervised an office which was manned 24 hours per day. The computer would be turned on at 0400 on 27 December one year and shut down at 2300 on 24 December the following year (as were many other PCs used by the company). Those PCs at work (which were all running Windows) never seemed to go wrong whereas all of the home PCs I've ever had seem to need System Restore or Scanreg run (or even Windows reinstalled) every few weeks. So, as far as the 'health' of the PC is concerned, I doubt that leaving it switched on will do it any great harm.
However, as others have said, it's far from being environmentally friendly. PCs which are not in use should always be shut down and switched off with the switch on the rear panel.
Electronically it does no harm to leave it on. Businesses have to leave their computers on permanently.
However, the continuous running of the cooling fans will wear the bearing quickly.
When your system gets noisy, check the cooling fans.
Interesting answer Chris, though I suggest that the problems encountered with home computers are more to do with willy-nilly installation of software and unnecessary "fiddling" than to do with turning on and off.
We always advise our customers to power down their machines at least once a month to reduce the memory leakage problems mentioned by fo3nix.
For anyone who doesn't know what memory leakage is:
Every time a program needs some memory (say as a buffer, or to create a button or window) it requests it from the operating system. When it no longer needs it it is supposed to inform the OS. If for any reason this doesn't happen, the memory is regarded as "in use" and is no longer available, so over time the free memory just gets smaller and smaller. The only way to release it is to restart.
another one is that the Power capacitors have a rated life (all be in 100k's of hours). Being on all the time can either extend or reduce there life depening on operating temperature.
If the comp goes into a silent standby (ie. everything stops) then its just put a copy of the RAM on the hard drive.
When it starts back up, the boot seqence basically says "put that info over there back into the RAM" this brings you back to where you were.
That doesnt solve the memeory leakage problems but it will use a few watts asopposed to a few 100watts.
A PC can easilly use 3-4kWh in a day if left on with no power saving. This is the same as 1-2hours of continual kettle boiling.
TFT monitors use much less than CRT so that would be a wise swap. I had 2x 17" CRTs which used 150w each!!! I now have 2* AGNeovo monitos which use 20w each at mid brightness.
If you have a CRT monitor, put a black screen saver on, they use 50% less power to despay all back as all white. TFT is constant power.
Powering down HDD's isnt a huge energy saver, they are about 10-15w each when just spinnig. Perhaps 20-25w when doing something.
The processor is the biggest guzzler - easilly 60w for a basic processor.
If laptop designers designed a PC, the whole thing would run of 20w at the same performance as the PC for ordinary tasks. Although the PC would be twice the price!
Im a turning off advocate. Esp as it stops malicious programs running without you knowing.