How many type of nuclear energy?

Nuclear fission reactors come in various forms, though the principle of using the heat from a nuclear chain reaction is always the same.

1. Pressurised Water Reactor (PWR). 2. Boiling Water Reactor (BWR). 3. Magnox gas cooled reactor (no longer built) 4. Advanced gas cooled reactor (no longer built but still in use in UK). 5. Canadian heavy water reactor (Candu) 6. Russian design of Chernobyl type.

I think this covers the most used types for power generation. There are others such as the gas cooled pebble bed reactor, and the fast breeder reactor, that are possible but designs have not been so successful and these have not been adopted commercially.