I just found out that Java allows enums to implement an interface. What would be a good use case for that?
It's required for extensibility -- if someone uses an API you've developed, the enums you define are static; they can't be added to or modified. However, if you let it implement an interface, the person using the API can develop their own enum using the same interface. You can then register this enum with an enum manager which conglomerates the enums together with the standard interface.
Edit: @Helper Method has the perfect example of this. Think about having other libraries defining new operators and then telling a manager class that 'hey, this enum exists -- register it'. Otherwise, you'd only be able to define Operators in your own code - there'd be no extensibility.