Incest

Although illegal in most parts of the world, the only real reason not to allow it anymore is the increase in potential birth defects of any offspring of such union, so if no offspring is ever conceived (wanted or possible) there's really no logical/rational reason to prevent it.

Historically this effectively denied political marriages, had the still present problem with higher potential of birth defects in the offspring which also reduced the viability of a family line for marriage into other families (thus a family line could die off due to inbreeding).

Note that the above mentioned birth defects can happen even without inbreeding or any other tampering (natural or not) and usually requires several generations before anything noticeable will happen. These are generally recessed traits already present in the family line. You're far more likely to get anything like this simply by drinking alcohol (or taking any other drugs) during pregnancy, even at "moderated" amounts, and that's just in one generation unlike what inbreeding requires.

Related:
* Lolicon
* Shotacon
* Porn