This heats water only when you need it.  So you save money and reduce waste by not heating and reheating the same tank of water.  This site claims a 40% cost in energy savings, lasts 2x longer than a tank water heater, and an endless supply of hot water.

http://www.rinnai.us/tankless-water-heaters/learn-about-tankless/how-tankless-works/


GB

I've used a tankless water heater and it works great. The best brand is Paloma. They're available at many RV supply outlets.

NOT AT ALL. So called in-flow heaters.I had such one and never again.This is a unefficient method of water heating.It was common in my country long time ago.When you open water tap,water begins to flow,then boiler fires-up.Depending from how far is your water tap you will wait for warm water coming.A lot of heat is wasted,combustion gases have still high temperature dumped to outlet funnel,in system like this you will never get to condensation point, to get to this point a heating coil needed to be very large. I would opt for a good condensating boiler with a optimal tank capacity,there are models that sucks nearly all of the natural gas combustion heat,going below condensation point not only in home heating mode,but also in water heating mode- in my opinoin the best is ACV Heatmaster 25TH,stainless steel, simple,without fancy electronic.Boiler has a very good insulation,so heat losses are minimal.Exhaust funnel from such boiler is also stainless steel duct-in-duct, so inlet air is heated by the outlet gases.When I place my hand above exhaust outlet I feel nothing.Second important thing- use programmer for hot water circulation pump,at night you don't need water circulation through system pipes.And of course,that pipes needs to be insulated also.
The easy way to see what boiler is good- just look around at the home funnels on the icy and sunny day.If you see steam coming out-that is all wasted energy.
From my Heatmaster I see nothing is steaming ot of the funnel :-).But I can see quite few liters of  condensed water coming from the boiler connection to the drain.

We use this in Europe now over 50 years (myself also)
the last boiler i seen  2 pcs installed the last 20 years .


the old boilers make losses an take time.


the 21 kW gas systems are also used for room / House heating
and bath / kitchen hot water.
the electric systems need near 10 Amp at 220volt 
that is not installed an all buildings
GP

http://de.wikipedia.org/wiki/Durchlauferhitzer  (german)