I would leave it on as long as power usage isn't an issue. I use sleep mode so I don't have to turn it on when I need to use it again.

As Potzato said, it causes fatigue to electronic devices to turn it on and off all the time so better use some kind of energy saving techniques and leave it on.

No I advocate not switching your computer off if you know you will use it one hour later.

It's not a 'do it and your computer will last a lifetime', because it won't. It's just an advice as to if you keep your computer idle for several hours (mine consume 120 W idle for instance) you put less strain on your components but you consume power. That's some kind of tradeoff, but that's more complicated : while running your ventilators get more dust, but I personaly don't care much about that because I am used to clean my pc.

Point is, I just said a fact about electronic device fatigue, now you need to use your good sense :-)

Edit : bonus question : do you know what is the consumption of your internet router/modem/box ? Do you keep it on 24/24 7/7 ?

If I don't use my PC more than 1/2 hour, I always turn off it. I personally don't see the interest to let it running for nothing, no matter its tasks ^^

I usually just put my computer to sleep when I'm going to bed or work, I rarely turn it all the way off. Power usage isn't really an issue for me, I'm just concerned about dust build up, especially since I have fans on the bottom of my case.

However, my girlfriend has left her computer on and running 24/7 since she got it a year ago, and it seems perfectly fine.

It is a good thing your PC is not HAL 9000.
So basically both options offers Pros and Cons.

Lots of theories around but I'm not aware of any serious tests. All I know is that in an office environment I never noticed a difference in hardware failures between PC that are always on and those that are shutdown at the end of every day. Business with lots of PC usually prefer them to be turned off at night to save electricity.

I personally put mine to sleep at night and reboot when asked too.

Difference between sleep and hibernation:

Sleep: That's like a pause function, the PC turn off every system it can without shutting down.

Hibernation: The PC saves its state to hard disk and then shutdown.

Mine goes into sleep mode after an hour of no use. I've got an SSD so its boots up in less than 30 seconds anyway. No idea what's best, though.

^^ This.

And I do shut it down if I'm going out and the weather looks like raining, as it may come with thunders or even power downs.

That puts more context on your previous comment.

As long as your computer doesn't overheat, I don't think it has a strong effect on the lifetime of your machine one way or the other.

For me, tt's about electricity and security.

No, there are some practical reasons not to:

1) Internally, our switch is getting on in age and doesn't handle re-setting internal IPs gracefully on reboot.

2) Our ISP doesn't provide us with a static IP and our external IP changes when our internet-facing router is rebooted, but otherwise, it seldom changes (and I take advantage of that fact).

I don't advocate going batshit crazy, but I think it's reasonable to take take some steps like shutting down your computer at night, turning off the lights when you are not in a room, don't buy a new computer/phone every year, buy digital whenever possible, etc. Just be environmentally aware and look for ways you can alter your habits to be more environmentally friendly.

My only computer is a laptop, and I pretty much never shut it off. The only time I ever reboot is for a kernel update, otherwise it is always just in suspend mode.

At most I put it to sleep unless I have a real reason to turn it off.

Since my gaming pc is also my television, newspaper, music player etc.
If I am at home and awake, it just runs.

This is usually from ~18:00 to 23:00, these five hours a day during the week.
If I leave the house for shopping or whatever on weekends, it is shut down.

I boot up my computer when I get up in the morning/noon/afternoon/evening.
I shut it down when I go to sleep or leave the house for an hour or more.

I let Settlers2 Anniversary edition run over nights :)