No, turn it off.
What computers do when they're on and not doing anything:
- waste electrical energy (which is not that negligible) <-- nowadays, wars are fought over energy, remember ?
- produce heat (which is not that negligible)
(neither of these are making our planet a nicer place to live)
- cost you money
What computers do when they're off:
- don't cost anything
- helps to ease up that air condition unit
- most of their parts are not made up for 24h work load
Hard discs do not suffer that much from turning off/on, as has been presented here. I've got three of them in the drawer/attic, which range from 15-10 years old, and have been turned off/on, regularly for 10 years, several times a day. All still work (I'm not using them of course, but they still work).
The price of energy has been calculated by someone already.