A popular belief amongst fans, perpetuated by commentary from characters in the books to show that it is widely believed in-universe, is that House Targaryen only ever practised incestuous marriage.
They certainly were fond of incest, and this was because of their Valyrian heritage. More particularly, their dragonriding heritage. This recently came up on /r/asoiaf where a new fan believed they had cracked a theory, but it’s actually just stated directly in the text: the dragonlords practised incest to maintain their ability to control their dragons.
That’s the why. This blog is about the who.