Tankless hot water heaters are the perfect solution for many household water heating problems. If your problem, is space, they are small. If your annoyance is running out of hot water, they are continuous. If your gripe is about cost, they can save you up to 50% over an electric tank.
The saving issue is simply because with a tankless waterheater you no longer have to keep a tank filled with hot water. Most tanks, even well insulated ones, have to switch on the heating element quite a lot to maintain the temperature that you have set. In other words you have a big tank full of hot water 24 hours a day.
What is even worse about a tank is that despite keeping all this water hot all day, when you need a lot in a short space of time, you can run out of hot water! With tankless water heater gas, oil or electric powered, you do not have problems with running out of water (you can run hot water continuously if you really want to). You are not paying for water to be heated when you do not even want the stuff. This is where the saving comes from.
They also tend to last longer that domestic tanks, which are only usually expected to last ten or fifteen years before they need to be replaced. Another benefit for your pocket.