Most hot water systems are either tank storage systems, or continuous flow systems (also known as 'tankless' or 'instantaneous' hot water systems). The type of system that's right for your home will depend on what sort of fuel is available, and how big of a demand there is for hot water in your home.
Solar, for example, demands that you have a tank storage system which can retain the water that's heated by the sun. Most continuous flow hot water systems in Australia operate on gas.
Continuous flow hot water systems are an efficient choice for households with 3 or fewer people. Most of them run on natural gas but they can also run on electricity.
Tank storage hot water systems are ideal for larger households. These systems can easily be used (or even adapted) to support a wide range of fuel types.
While still a relatively new type of hot water system, hybrid tank/tankless systems offer the best of both types of systems to efficiently provide constant hot water.