Say I have a type which can be an integer or an enumeration, would it be possible to do:

@NotNull @Min(0) @OneOf({Integer, MyEnum}) Object foo;

(@OneOf is an example, and gives a list of acceptable assignable types )

It looks like constraints are advised to accept null as a value to allow NotNull to work, but to fail if data is not of a type that the constraint can handle.

Are constraints meant to ignore data that is of a type that isn't accepted, or are these cases expected to be handled by custom annotations?

@OneOf really is meant to accept all types and return true only on a subset of types.

I think generally speaking the spec recommendation is good. If the validation logic does not expect a given type, it should raise an exception. For example, let's say you apply @CreditCard on an URL object, an exception is thrown.