Does turning a computer off and on throughout the day damage it? Why, or why not?

It won't neccessarily damage it but it will accelerate wear on things like the on/off switch and the hard disk.

The hard disk has to spin up every time you switch it on, and in that process uses far more power than just bringing out of sleep or hibernation.

As Trekdozer says - sleep or hibernate if not being used during the day - switch off at night if you want to is the best plan. You need also to be aware that there are processes that go on while the machine is idle - disk defragging being one of the most important..

If it's just a few hours or even overnight, it's usually more efficient to put your computer to sleep, either by clicking the Power button on the Start menu or by closing the lid on your mobile PC. (Some computers also have a dedicated sleep button on the computer case.)

There are several advantages to choosing sleep over shutting down:

• All your work, including information about the programs you were using such as window location and size, is automatically saved.
• When you awaken your machine from sleep, you don't need to restart programs or reopen files as you would if you had shut down the computer.
• While Windows does use some power in sleep mode, it's very small: about one-tenth as much as it would need if you left the computer running. A mobile PC typically uses 1 to 2 percent of battery power per hour in sleep mode.
• When Windows is asleep, it can still download and install updates and perform other routine maintenance tasks. For this reason, some companies require employees to put their computers to sleep rather than shut them down when going home for the evening.

But there are instances when you should shut down your computer fully—for example, when you install a new memory card or other hardware. If you don't plan to use your computer for several days or more, you should also shut it down.

Turn off a computer: frequently asked questions:

http://windows.microsoft.com/en-US/windows-vista/Turn-off-a-computer-frequently-asked-questions