When we lived in South Africa, we had a 500Litre boiler that was always on.
But it was insulated by the factory and the theory was that on night tariff 23:00-4:00, at 80% cost, we could heat the water up to 80degrees and before it reaches 22:00 the water is still 50ish degrees celsius. But if we used up the water we would have to manual override it and get it to heat up again, so we just left it on the whole time at 65 degrees. We didn't notice a bit difference in bills since the theory was that the insulations kept the water warm.
In England, they use a tank system with a GAS burner. The water gets heated by pumping water from the tank into the boiler over and over until it gets to a certain temp. We also have this insulated, not as well as the one in South Africa. Its cheaper because its GAS.
New energy efficient, condensing combi boilers, heat water on demand, when you turn the tap on but it takes some time to get to the tap though, so there is some water waste. But you can get inline electric water heaters, like in showers, but now under your sink and heat water right by the tap so you do not have to drain litres before warm water comes down. It think these are the most efficient ways to save on energy, since the water is heated right by the sink, and they are really efficient too!
It all depends where you live. If you live near a Hydro plant and you get electricity for 80% discount, then you can just use electricity to heat everything, day and night, but in England, where energy is the most expensive in the world.. we sometimes prefer a warm Polish Wool blanket!