With tank-type heaters, water is heated, it sits there cooling off in a big tank, then it's heated up again and it sits there cooling off. How smart is that?
The United States is one of the few countries that still uses tank-type water heaters, because, historically, our energy costs have been so low. Other countries figured out the virtues of demand water heating a long time ago. Tank-type heaters use a minimum of 20% more energy than demand systems, due to heat loss. Small one- or two-person households, have even greater heat losses, because the hot water spends more time sitting around, waiting to be used.

tankless (demand) water heaters
Tankless heaters are moderately priced, long lived (20 years), and, next to solar, have the lowest operation costs making them the best choice if you have either natural gas or propane as your fuel source. Solar water heaters have become very efficient and cost effective. We recommend using a both in tandem for maximum efficiency.

The advantages of demand water heaters:
• very low standby losses
• lowest operation costs
• unlimited amounts of hot water delivery
• a very long life expectancy

Disadvantages:
• they only run on natural gas or propane
• they cost more initially
• flow rates can be limited, depending on unit size

how demand water heaters work Taken from Real Goods article: Common Water Heater Types
Demand or tankless water heaters only go to work when someone turns on the hot water. When water flow reaches a minimum flow rate the gas flame comes on, heating the water as it passes through a radiator-like heat exchanger. Tankless heaters do not store any hot water for later use, but heat water only as needed. The minimum flow rates required for turn-on prevent any possibility of overheating at very low flow, and ensure that the unit turns off when the faucet is turned off. Minimum flow rates vary from model to model, but are generally about 0.5 to 0.75 gpm for household units. Other safety devices include the standard pressure/temperature relief valve that all water heaters in North America are required to carry, plus, tankless heaters use an additional overheat sensor on the heat exchanger.
The great advantage of tankless heaters is that you run out of hot water only when either the gas or the water runs out. On the other hand, tankless heaters are limited to a fixed output in terms of gallons per minute. Excess water flow will result in lower temperature output. So most tankless heaters are limited to running just one fixture at a time. Larger heaters can run multiple fixtures simultaneously, so long as one of those fixtures isn't a shower, where things get quite temperature-sensitive. Tankless heaters are probably the best choice for smaller homesteads of three people or less where hot water use can easily be coordinated. Larger homes with an intermittent use a long distance from the rest of the household hot water plumbing, such as a master bedroom at the end of a long wing, are also a good candidate for a tankless heater just to supply that isolated area. Most tankless heater units are thermostatically controlled. At lower flow rates the gas flame is automatically reduced to maintain a stable output temperature. The temperature is front-panel adjustable from roughly 90°F to 140°F. (120°F is an optimal setting.) If the water flow rate increases, the heater will respond by increasing the gas flow, up to the heater's Btu maximum. This makes a heater that performs more like the storage tank heaters we're all used to. The system isn't perfect, the sudden opening of a second tap will still cause the shower temperature to fluctuate. But this is also true of the plumbing in most homes with storage tank heaters. With any tankless heater , we recommend only running a single fixture, if that fixture is a shower since this is the best way to ensure a steady temperature. Some units have built-in flow restrictors so that it is difficult to run more water through the unit than it can heat. If too many taps are opened simultaneously, the water pressure will fall and the water will simply run lukewarm, rather than ice-cold.

An advantage of tankless heaters is their life expectancy. Demand heaters are designed so that all parts are repairable or replaceable. Many companies warranty their heat exchanger for a full ten years. There is no reason why these heaters should not last the rest of your home's life. Compare this to tank-type heaters, which have a 10- to 15-year life expectancy at best.

solar water heaters
Solar water heaters are expensive initially, but their long life expectancy and nearly zero operation costs give them the lowest life-cycle cost. There are several high quality solar water heaters on the market that are warranted for 5 to 10 years and sold by solid companies. These water heaters can be expected to last as long as your house. Some models are very simple, others use controllers, sensors, air vents, or draindown valves. Complex hardware is more prone to breaking down. The more simple heaters use passive design with sunlight and heat as the controls.