From Unchecked Exceptions -- The Controversy:
If a client can reasonably be expected to recover from an exception, make it a checked exception. If a client cannot do anything to recover from the exception, make it an unchecked exception.
Note that an unchecked exception is one derived from RuntimeException and a checked exception is one derived from Exception.
Why throw a RuntimeException if a client cannot do anything to recover from the exception? The article explains:
Runtime exceptions represent problems that are the result of a programming problem, and as such, the API client code cannot reasonably be expected to recover from them or to handle them in any way. Such problems include arithmetic exceptions, such as dividing by zero; pointer exceptions, such as trying to access an object through a null reference; and indexing exceptions, such as attempting to access an array element through an index that is too large or too small.