I like to cut the power and close the tank ball valves when not using mine. Consider cases of a blown out hose, or other pressure line where the compressor runs non stop until its noticed. Happened to a buddy of mine, a line blew sometime between Saturday afternoon and Monday morning when he was back at the shop.
Funny story about that.
About a year ago, I bought a $25 pan/tilt IP camera on eBay, and mounted it upside down to the underside of the attic ladder that goes up to the loft in my garage (because that spot had the most central and unobstructed views). The compressor is in the loft...
I have the camera set to email me a snapshot whenever it senses motion. Kind of a cheap security system supplement. Usually I'll just capture a picture of the wife digging through the freezer. After I'm working in the shop, I'll delete a few hundred **** emails, etc.
Well a few months ago, while at work, I started to get an email every few minutes. After about 10 of them, all with the lights off, I knew something funny was up. Then I noticed that every other image had a vertical motion blur, and the other half were clear. I thought that perhaps an animal was trapped in the loft and was walking on and off the closed ladder...
Then I got the good idea to log into the camera and pan around a bit. When I saw a plastic bag fluttering around on the workbench, I immediately realized a compressor line had blown, and the running compressor had vibrated the loft floor just enough to trigger the image motion detection.
A phone call and a few minutes later, and the coil hose that had split was shut off, and all was well in the garage again.
Now I know that if I get a motion detection email with the lights off, I've got a leak somewhere.
But in regards to the OP, no, I leave everything on. I only drain water from the tank as needed.