Everyone loves the feeling of warm water available from the faucet when you want it. But did you know there are actually a lot of different ways to provide that to you?
Conventional water heaters: These have a glass-lined, insulated tank with a source of heat to keep the water warm all the time. There are, or course, "standby losses", meaning that the heat slowly escapes and has to be replenished by cycling the source of heat on and off as necessary. The common sources of that heat here in the Northeast are Fuel Oil, Propane, Natural Gas, and Electricity.
Electricity has historically been the most expensive of these choices, though the cost of the heater itself is the cheapest initially. They have an electric heating element submerged in the water inside the heater. Overall, it's a pretty expensive way to heat the water you need for washing, showers, and so forth.
Gas - Either Propane or Natural - is the next in line in terms of equipment cost. They heat water very economically and their "recovery time" (the time it takes to heat the incoming cold water so you don't run out) is much faster than with electric models.
Fuel Oil - this is the most expensive type of heater at initial purchase. They burn cleanly and provide the fastest recovery times.
Indirect water heaters: These look very much like a conventional water heater, using a glass-lined, insulated tank to store the hot water. The difference is that they do not have a burner (like gas- and oil-fired heaters do), nor do they have an electric heating element submerged in the water. They have a copper coil that receives hot water from the boiler used to heat the house; the heat is then transferred to the water in the tank so you can use it from faucets. Of course, you must have hot water heat in the home in order to do this.
Tankless Coil: This is a copper coil inside the boiler used to heat the house. It's submerged in the water inside the boiler, and therefore the water coming out is extremely hot. That hot water is then mixed with some cold water to provide the proper temperature at the faucet. No hot water is stored, so there is no standby loss from the water heater, though there is standby loss from the boiler, and the boiler must be run year round so you'll always have hot water. These type systems require a flow restrictor so the water can't be drawn faster than the boiler can heat it.
Tankless On-Demand water heater: This is a great way to go! There is a unit about the size of a medium-size duffle bag, usually mounted on a wall, with a super-efficient heat exchanger. When you turn on a faucet, the burner fires up and heats the water as you use it. When properly sized, they provide endless hot water, yet when the faucets are closed, there is no tank full of water just slowly cooling off that you then have to pay to re-heat!
One more thought: If you're building a new house, or have a single-story home with open access in the basement to the plumbing overhead, you can install a "circulating loop" of insulated pipe that essentially keeps hot water literally instantly available at each faucet as soon as you turn it on. No more waiting several minutes for the hot water to get from the water heater to the faucet!
This concept can be incorporated into any of the types of hot water listed above except the tankless coil. It's the epitome of convenience in larger homes where the water heater might be a long ways from some of the faucets.