Incest in an Elevator
The other day one of my seminar groups spent a good half hour discussing whether a Millian state could prohibit incest. It's actually an example I've used myself in lectures (though not this year). For what it's worth, I think the answer is no: such interference would presumably be moralistic (or perhaps paternalistic) - it's unclear that it could count as harmful since, even if a deformed child is born as a result, that child would not have otherwise existed (and therefore cannot be harmed) and, in any case, no child need result, so at most the state should prohibit incestuous couples producing children, rather than incestuous relationships per se.
It seems that, while our state may be more liberal than in Mill's day, incest is still punished by both the courts and society, as this recent/local example shows.