The main damage is to your electrical bill. I'm no hardware expert, but I fall into the camp that says leaving it on 24/7 extends the life of a computer. My main home computer is basically five years old, only replaced a fan or two, the psu (low cost earthwatts one to save $) and a cpu upgrade (not needed, just wanted) and adding a second internal hard drive.
My sister, OTOH, who is a firm believer in turning off her computer is she isn't going to use it for a couple of hours, has replaced or fully rebuilt her computer at least three times in the same time period.