Always power strips (or outlets on a switch, wired properly), too. Who knows what shape the wiring is inside of the machine and even then inside the insulation. I never ever ever leave power running to a game at night with it switched off. Not worth the risk. This very strictly goes for all 30 in my collection regardless of age or condition. Thankfully whenever I have slipped up (games switched off by their switch though, of course) things have been fine. Most machines even when switched off run power to the service outlet (so you can plug in your light/soldering iron with the machine still turned off) which runs through a fuse block, etc., etc.. There's still a lot of power in these things even when you think they are totally off.
But yeah, on and off probably adds some stress but we all do it anyways. Maybe leave it on if you're going to grab a drink in the next room over and then come back with it, but don't feel obligated to leave it on from 12 PM to 10 PM just because you're going to play twice a day. Waste of energy, and waste of running a machine. As for leaving them on TOO LONG, I have friends who run arcades and these things are on 11 hours a day all day with no gaps. It's what they were built for. Just watch over for screen burn (and your electric bill), and on pinball machines hot bulbs left on for a long time will destroy backglasses, plastics, and inserts over time. Again, not worth it "just to do it", but if you're having a party or something don't feel bad about it, it's what they were made for and I do it regularly when walking through my arcade or even just sitting and looking, they're all on at once. (Of course!)
Probably would take a long time to damage a game from turning it on and off with normal hobbyist use, even if more frequent than back in the regular arcades.