I have heard several diffrent things and I was wondering what the pros and cons are of leaving it on vs turning it off.
Leaving it on can strain the hardware less, and it's quicker to accsess. Other than that, I dont know. Dont forget, the strain on the hardware by stoping and starting isnt much. Unless you do it every few minutes.

If you ask me, your better off turning it off if you have no need for it to be on.
In response to Smoko
I get more dust in my computer when I leave it on 24/7.
Personally, I never turn mine off when it's not in use. I've had this same computer for years, and it hasn't been damaged by it yet -- I'd say the so called "damaged" it gets from being left on is so harldy noticable that it wouldn't matter.

I'd think the stress of the computer booting up would be more than leaving it on! :P

I usually turn it off, especially if I just finished playing a big game (i.e. Half-Life 2, World of Warcraft, etc.) because the computer needs to cool off a bit. You cannot let the fans do all the work for you, that is how the computer can damage. But since my laptop is in my room, I usually turn it off so it does not keep me up when I try to go to sleep.
In response to Digital Samurai
Your fans are probably only sucking air in and not blowing anything out. It might help to pull the panel off the front and crack open some empty drive slots. It should help the air go through it.

One big problem I have with leaving it on is that my room tends to get very hot, so even when it's idling over night it doesn't cool off much.
I've got the temperature alarm going. So it wont over-heat without beeping for a few hours before hand. That's another reason why I try to keep the air flowing through it as smoothly as possible.
In response to DarkView
I had to remove the fans in my pc cause of a new processer and I never bothered to put them in. I just leave the case of.
If it's a desktop PC with decent fan cooling, you're better off leaving it on in the long run...

The worst of the wear and tear comes from heat shock... Going from dead-cold to running (and back again later) causes rapid expansion and contraction of the components and circuitry in the machine... Over time, this wears them out (just like a light bulb blows out sooner from being turned on and off too many times)

I would imagine that another danger is electric overload... Each time you fire the thing up, it takes a fairly large jump of electricity to get everything going at once... This spike may run the risk of damaging things (they're designed to guard against this, but it's still possible, and every time you turn it on, you have a small chance of it occuring)...

So, as long as your PC isn't overheated (to the point where the CPU and other heat-sensitive parts are in danger), it will cause less damage overall to just leave it on all the time...

Now, in the case of things like laptops, where the cooling isn't the greatest, it's probably a safer bet to turn them off when not in use (the damage caused by constant heat is a greater risk than the wear and tear caused by constant start ups)

[Edit:] Of course, it's necessary to add that between the two actions, you'd likely only notice any difference a LONG way down the road... Usually longer than you'll have that particular machine...
I leave mine on all the time, my computer runs pretty cool so it's not a problem.

From what I remember the con of leaving it on is that the harddrive is supposed to malfunction faster(though it's never been a problem for me).

The cons of turning it on and off is that the electrical shock sent through the system supposedly reduces the life expectancy of your components each time it happens.