Final Fantasy IX: Zidane's a lab experiment; Vivi's parentage is a complete mystery but it's heavily implied he has no biological parents; Garnet's mother dies, then her adoptive mother dies too; Steiner's parents are never mentioned; Freya's family are never really mentioned as far as I can remember; Quina... well nobody has a clue; Eiko is an orphan living on her own in a deserted village; Amarant doesn't seem to wanna talk about it.
It's not a complete mystery at all. Kuja created him from mist. Vivi fell off the cargo ship in front of Quan's Dwelling and Quan took him in for a few months before dying himself. Quina is her own parent, because from what I heard I believe Qu's reproduce asexually. In all of the games most of the time parents aren't mentioned like the majority of characters you put up there.