I work in a few schools where children have been taught to turn off the monitors to save energy. Unfortunately, this is all that they turn off. Every Monday morning I find 30+ computers running with powered down monitors.
What is best for the greater good?
Train them to shut down and leave the monitors in hibernation or, shut the monitors down with the risk of the hard drive and processor running for days on end?
We had the same issue at our high school a decade ago.
The best strategy is to power down the computers and let the monitors go into standby mode. Computers consume far more power when idling (30–100W depending on faculty) than monitors do on standby (~3W).
Don't rely on sleep/suspend/hibernate features for saving power overnight or over weekends. The inevitable brownouts and blackouts that occur will corrupt filesystems and damage hardware. The aggravation that causes — and the time/money needed to deal with it — is just not worth it.
A student-reliant approach can be problematic, though. Sometimes kids will press the power-off buttons but the computers won't turn off (for a variety of reasons). Sometimes a display will be off/dark so it already looks like the computer is off so kids don't bother pressing the button. Sometimes someone has forgotten to save work and log off, so the shutdown fails. Sometimes the computer is already off, so pressing the button actually turns it back on again. Sometimes kids are sick, so classes aren't full, and so not all of the computers are being used, so not all of them get turned off. The list goes on.
We tried for years and failed.
Eventually our IT technicians modified the Windows disk images to include a scheduled service that called Shutdown.exe at the end of the day — forcibly shutting down all of the computers 15 minutes after the kids went home. Problem solved.
Anyone who was still working at a computer got a "This system will shutdown in 60 seconds" warning that gave them the option to abort the shutdown... so it wasn't an "instant-off" type of thing.
If you want to maintain some level of manual control (for whatever reason), but don't want anything that is too technical, look at programs like Advanced IP Scanner http://www.advanced-ip-scanner.com/ — it can run from a USB flash drive, can scan your entire network to work out what computers are still on, and let you turn them off remotely (assuming you have the credentials). You can still have the kids turn most of them off, but one teacher can then catch the strays from anywhere on the network before locking up and going home.
Turning the screens off and leaving the computers on is a bit like stopping a dripping tap while leaving another tap gushing!
Assuming they are LCD, monitors won't draw much power (other than to power a single LED) if they are not getting a signal.
The computers will draw vastly greater amounts of power over a weekend if left on.
However, if the PCs are in sleep mode or hibernate over the weekend, they will only use trivial amounts of power.
Bottom line, don't worry about the monitors, just make sure the computers are off or asleep.
The power consumption of an old monitor is nearly the same when compared to the power consumption of an old tower PC. Similarly, the power consumption of a recent monitor is nearly the same when compared to the power consumption of a new tower PC. Ok, in some cases, the tower PC could consume bit more power within a factor of less than 2. I wouldn't claim that a computer uses "far more power" than a monitor, as claimed in the upvoted answer. Actually, today, when many prefer laptops, the big power user is the monitor and not the computer.
I'd say if your goal is energy saving, the computers should be turned off when not used for a certain amount of time. So, for example, during weekends, they should be turned off.
I happen to have three monitors (23 W per monitor) and a very modern low-power laptop computer (probably only few watts of electricity used) to which they're attached. I always turn off the monitors but don't turn off the computer as it uses so little power as a laptop.
Next time when renewing the computers, you could consider replacing the tower PCs with laptop computers attached with a lock to a secure object (so they won't be stolen). Most laptops have an ability to attach an external monitor. When selecting a laptop, place an emphasis on good battery life (which may mean either big battery or low power use) and low weight (which will filter out the ones having big battery).
Also, the choice of laptop allows them to be used as laptops as well, meaning if you require both fixed computers and laptops, the same computers can be used for both purposes. Less materials used, less damage for the environment. Less weight, less emissions during shipping the computers from China to wherever you happen to live.
Furthermore, during electricity breaks, laptops have far better characteristics. They can survive minor power breaks without filesystem damage, and in the case of major power breaks, they will typically shut down in a controlled manner (no filesystem damage) when there's only few percent of battery life left. About the only drawback of laptops is that when performing heavy computing, the fan will spin like crazy!
