I used to turn it off at night (except for my weekly scheduled Norton scan which is set for the early hours of the morning so it doesn't slow things down if I'm using it). I thought this was just common sense like not leaving my TV on while I'm at work all day.
However, a couple of months ago I turned the computer on when I got home and it wouldn't boot, just kept restarting and restarting but never getting there. I ended up having to buy a new hard drive. My computer tech (a friend who fixes computers and knows what he's talking about) said that many computer problems are related to start-up and that he leaves his on. So now I do the same but reboot now and then to give it a fresh start when I feel it's getting slow and bogged down with temp files etc. (I turn it off for 5 minutes, as distinct from restarting). I do this maybe once a week, no set rule.
My job is with a small firm with 6 computers and we turn them off (except for the 'server' computer). Don't know if our IT guy suggested it or not. I've also worked in large companies like banks and insurance and it varies a lot - some turn them off, some don't. But are there computers in the IT office that do a major backup and stay running? I have no idea!
As for sleep mode etc., when I go away from my computer for a while, the screen saver works at first and then reverts to that screen showing the user name. Don't know what power-saving mode this is and can't seem to find how to make the screen saver stay on all the time, like it used to do with XP (I'm now on Windows 7).