Bruce Wayne: Despite the many continuities Bruce usually has a father/son dynamic with Jason. I've talked about this a lot in other posts but I always loved the complex relationship between the two. What's interesting about this is Jason was actually the first of the bat kids to be adopted.
Joseph and Trina Todd: The acrobats. When Nightwing asked for their help it ended with Jason becoming an orphan. Killer Croc was their murderer and as a result Dick considered adopting their kid.
Nocturna: I want to eventually write more about her and the other pre-Crisis entries. I'll probably wait until I review those issues. She wasn't like the version that appeared in Batwoman. Nocturna adopted Jason for awhile, she was kind of like another Catwoman (stealing/romance with Batman) and viewed him as her son. After awhile the feeling was mutual.
Catherine Todd: Jason's step mother in old canon and birth mother in New 52/DCYOU canon. It's odd but how she died changed during Jasons' Robin run. It was either an overdose or later it was changed to her having an diease. Maybe a misunderstanding to do with Jason claiming she was sick although Bruce confirms it was a drug OD soon after. The drug usage is currently her backstory. Whatever the mother/step-mother canon Jason loved Catherine despite her faults.
Willis Todd: There was some debate about Willis as many believed he couldn't have been a bad father since Jason cared so much about his death. There were also pictures Jason looked at during DITF hinting that in the past Willis had been more loving. I didn't mind the later more jerky take on Willis as we barely knew anything about him.( Although he was a HUGE ass in RHATO VOL. 1 flashbacks.) Plus Jason still seemed to see Bruce as more of a dad than his flesh and blood. Anyway Willis was barely ever home as he was in jail half of the time. In old canon worked for Two Face before being presumably killed by him. In newer canon Willis was a drug dealer.
Shelia Haywood: Jason's birth mother that infamously handed her kid over to the Joker when he was trying to save her. Then smoked while he was being beaten. There has been theories of her not being his actual mom even before her story was merged with Catherine's in the new 52. I didn't mind that much since Shelia was only in one story arc. She did appear in a Deadman mini series issue although that painted her in a worse light. It revealed that Boston had possessed her to try to save Jason meaning she literally did nothing to try to help her kid.