Today I was browsing through some questions on this site and I found a mention of an enum
being used in singleton pattern about purported thread safety benefits
From Java documents -
You should use enum types any time you need to represent a fixed set of constants. That includes natural enum types such as the planets in our solar system and data sets where you know all possible values at compile time—for example, the choices on a menu, command line flags, and so on.
A common example is to replace a class with a set of private static final int constants (within reasonable number of constants) with an enum type. Basically if you think you know all possible values of "something" at compile time you can represent that as an enum type. Enums provide readability and flexibility over a class with constants.
Few other advantages that I can think of enum types. They is always one instance of a particular enum class (hence the concept of using enums as singleton arrives). Another advantage is you can use enums as a type in switch-case statement. Also you can use toString() on the enum to print them as readable strings.