Maybe. It depends.

The issue isn’t as simple as you might think; there’s no single answer to this perennial question.
My answer, naturally, is “It depends.”
There are two issues at play here: the power used by a computer left running 24 hours a day and the stress on hardware components being repeatedly turned off and on.
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Turn computers off at night?
Turning your computer off at night can save power, but standby mode uses almost as little energy. Turning the machine off and on over time repeatedly could stress some components, leading to earlier replacement. However, modern parts are built for this. With no simple answer, decide based on your usage. In particular, prioritize whatever enables automated backups; they’re important.
Power consumption
Power consumption is the easier question.
In most cases, standby is almost as good as turning your computer off completely. The computer uses a little power to keep itself ready for use, but components using the majority of the power, like spinning hard drives or display devices, are turned off.
Of course, turning the computer off completely prevents power from being consumed at all.1
Before you decide that standby or power-off is what you want to do to save electricity, it’s important to realize that your computer may already be taking steps on its own to minimize power usage when you’re not using it. Many individual components go into the equivalent of standby on their own if they’re not used for some period of time. Hard drives may turn off after some period of inactivity. Screensavers eventually turn video displays off. Even a wireless mouse or keyboard may assume a low-power state when they haven’t been used for a while.
Depending on your computer, it’s quite possible that simply walking away reduces the amount of power being used.
Stress (the computer’s, not yours)
There is an argument that says leaving a component on continuously is less stressful than turning it on and off repeatedly. While you may save power while the device is off, the stress of heating up and cooling down over and over when starting and stopping can contribute to earlier failure and required replacement.
The argument is that the cost (in terms of purchase price and the environmental impact of replacing a broken component) is so high that in the long run, it would be more cost-effective to simply leave it on all the time.
The counterargument is that most components are built with this in mind. As I mentioned, many components turn themselves off after some period of inactivity, whether you tell them to or not. The devices are built to power cycle fairly frequently.
And in almost all cases, devices already last longer than we need them. Devices are most commonly replaced not because they fail, but because newer and more powerful devices are purchased.
What I do
As you can see, there’s no simple answer. There are arguments for both approaches.
My approach is to ignore all of the arguments above as they more or less cancel each other out. Instead, I make the decision based on how I use my computers.
It’s no surprise that I am a heavy computer user, and for me, the answer is to leave almost all of my equipment running 24 hours a day. Not only does that keep everything ready and running for my use, but it also allows automated processes like updates and backups to happen in the wee hours of the night when I’m asleep.
Do this
My expectation is that an average user who uses their computer a few hours a day would most likely turn it off or put it into standby when it’s not going to be used for a few hours or more. That’s simply to minimize power use. It’s also not a big deal if you don’t.
If you use it longer, perhaps you leave it on all the time. Again, no big deal.
If there’s anything I might consider a tipping point in the decision, it’s backups. If leaving your computer on all the time allows you to automate the process and take backups where you otherwise would not or would forget, then in my opinion, it’s worth it.
Backups trump everything.
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Footnotes & References
1: Surprisingly, not quite true on some machines. Even when you turn the power completely off, there are often components that remain powered to some degree. Only pulling the power plug prevents this tiny trickle of electricity from being used if it is on your specific machine.