There are arguments on both sides of the question - on because it does not hurt the CPU as much, not as many cycles and not as hard on the hard drive. Off because it saves energy.
I have three at home and one of them is always on. Of the other 2 - one is laptop so that is another issue- and the othr an older one I use for certain programs.
"There are two means of refuge from the miseries of life: music and cats" Albert Schweitzer