This conversation always needs to have 'off' and 'on' defined'. If 'off' means 'no blue light', then what SkiTyke says is correct. It's not really great to have the harddrive reading/writing all the time. Having the RTV itself powered on (which it is all the time) is not a bad thing. I've got PCs on UPS's that have been running for years without problems. They aren't actually doing a lot, but having harddrives spining? Not a problem. Actively read/write all the time? Not a good idea, especially if you aren't watching the TV, why bother.
The other reason (semi-asked in other threads) to not spin the harddrive down when 'not used' is to not have to spin it up when starting a recording (the whole (well, one) point of an RTV). Remember, most failures occur on startup, not while running!
My bottom line: four RTVs, always 'running', 'blue light on' only when viewing that unit. Never a problem.
(And, my sat boxes are all on all the time, of course. No problems with them, either. No moving parts, of course, there!)