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Actually, there are cases when it is safe to turn off the computer (after the OS has been properly shut down and all filesystems will not be written again).

However, it's risky to turn on the computer! Like all other electrical instruments, computers and their peripherals tend to break most often right after turning them on - it's about the "running temperature" and "cold start", see? Light bulbs burn most often when the lights are turned on - it's the same thing with computers.

Due to this small risk when turning on the computer, it's often recommended to leave the computer on during long periods of use and only turn it off when you're not around - server machines, of course, should be running continuously. Shutting down for cleaning/hardware installation is the only really good excuse. If you're concerned about power consumption, consult the documentation for power saving instructions (most machines these days support some sort of standby mode).

See also: Is it better to turn off your computer at night, or let it run all the time?