Bloodlines often pass down certain traits and abilities in the series. Some have strong sixth senses, others mind-reading, knowledge, a curse or duty. It might not be all grim if you had the chance to access that family's history though...
Which family would you be a part of, if just for a day?
I'd have to go with the Mikomori maidens because I'm just too in love with Glancing and Shadow Reading to choose anything else. Imagine how useful they could be! On the other hand, descending from the Munakatas or Shadow Priestesses could lead to some interesting discoveries.
I guess the real question is, who'd risk becoming an Asou to get all his secrets?