On Google+, Rona answered this question:

Several years ago, our tank water heater failed rather spectacularly, gushing water all over the basement floor. This morning at 6, I put the skills from that episode to work as, half-awake, I turned off the water and the pilot light for our neighbors’ tank water heater, which at least was failing slowly enough that there was only about 3″ of water on the floor. This is the kind of thing that makes me think that I will install a tankless, on-demand water heater when I am master of my own real estate. Is this as sensible as it sounds, or is this just my irritation making my decisions for me?

There are two unrelated factors in your post. First, you can prevent flooding from conventional direct gas-fired hot water heaters. Direct-fired hot water tanks are designed to fail. They have a fiberglass coil that erodes because of minerals in the water. A tank with a five-year warranty will last a bit over five years. A ten-year tank costs more, and takes about ten years to fail.
The second, has to do with the inefficiency of that appliance. Direct fired hot water heaters are energy hogs (even the so-called efficient ones) because they boil water 24/7, when we typically don’t use hot water all day and all night. A more efficient way to create hot water (especially in the winter) is to heat water for showers and dish washing using the heating boiler. This can be done by a so-called “tankless coil.” This is not what I think you are referring to. This kind of tankless coil superheats a small volume of water, which mixes with cold water to supply hot water for showers and dish washing. Once this water is used up, it takes some time to resupply the superheated water. For larger households, this can be a problem. The solution is to add a storage tank holding water heated from the boiler. This is called an indirect hot water tank. This system burns far less gas than a direct fired hot water heater. Also, the direct-fired tanks fail more frequently than the indirect, so they are more costly in that way. I think the hot water system you are coveting is a demand-type/tankless system.

For a household that has moderate use of hot water the demand-type systems are most efficient. They are sometimes called “tankless,” thus the confusion. These heaters superheat small quantities of water, as it is needed. This saves a great deal of energy. They don’t require the boiler to run all summer (as in the tankless coil or indirect tank,) nor does the pilot light stay on 24/7/365.4 like the conventional direct-fired gas hot water heater. Demand-type hot water systems last a long time, which helps make up for their hefty installation cost (about $4000.) If you are going to live in your castle for more than 10 years, you will benefit from the saving by installing a system like that.