Actually String is not immutable if you use the wikipedia definition suggested above.
String's state does change post construction. Take a look at the hashcode() method. String caches the hashcode value in a local field but does not calculate it until the first call of hashcode(). This lazy evaluation of hashcode places String in an interesting position as an immutable object whose state changes, but it cannot be observed to have changed without using reflection.
So maybe the definition of immutable should be an object that cannot be observed to have changed.
If the state changes in an immutable object after it has been created but no-one can see it (without reflection) is the object still immutable?