Yes and no. Turning it off will allow it to cool down. I have a power laptop and if it has been on all day encoding video or whatnot the body can be hot to touch. Turning it off will let it come to room temperature. Also the backlight to the screen usually is rated to 30,000 hours so if on all the time you can quickly kill one.
A processor can burn out quickly too. Not got a mean time before failure (MTBF) on them but I have seen people kill them in 2 years with being on all the time. But expect 5 years of non stop use at most.
Then the hard drive. I remember reading these are rated to last 1billion (12 '0's) spins. Thats 2143 days of non stop spinning. So over time these things die. I turn my laptop off every night unless it is encoding something however I have already killing one hard drive in 4 months.
Turning a computer of any sort on will also eventually be its demise as the sudden input of electricity adds wear and tear. Not much but over time it adds up.
Best to turn it off however in my opinion a little rest does it no harm. Very few machines are expected to run non stop why should one of your most expensive items be expected the same of.