As far as lights go....
the light bulb itself will last longer if turned on and left on.
What wears a lightbulb out is the change in state and the change in heat.
Incandecent bulbs were cheap enough to replace, and inefficient. So it was far cheaper to replace the bulbs than 'waste' the electricity.
Flouresent bulbs worked differently, although the ballasts inside are rather pricey. It would be a hard call as to what costs more- running the lights constantly, or replacing the bulbs and eventually the ballast/fixture.
Even worse are those stupid curly flouresent bulbs that replaced the incandessents in our lamps and other fixtures. These monstrosities used rather little power, but often cost $10 each. The worst part of it was that they were advertised to last for many years, and most often you were lucky if you got one or two years out of them.
Oh, yeah, and just like the other flouressents, they too have mercury in them, so ther is that as well.
Probably better to turn those on, and leave them on. It will take a bulb like that its lifetime to burn the amount of electricity that would equal the cost to replace the bulb.
And now we move on to the LED replacements for our lamps and such.
So far, so good with these.
They use very little power, and are much more pleasing to the eye than flouresents.
But, they do have a tendency to flicker sometimes, and the cost is astronomical.
So it is safe to say that it is cheaper to leave these lights on, than to wear them out from cycling on and off.