I don't know why, but I always find myself interested in stories where some (relatively) older guy/man starts to look after a younger girl under abnormal circumstances. My interest requires no Usagi Drop style ending, however. Albeit the ending is of course unknown while browsing series, so retaining my interest could be a better way of expressing it.
Maybe it's because Aishiteru ze Baby was quite an early anime for me, leaving me impressed. It holds a permanent place on my top list. It could have affected my tastes in anime/manga.