Family units of various DC superheroes, that I know of:
Superman’s adoptive parents are still alive and well - and raising Superboy, who is, in a way, his son.
Tim Drake (the current Robin)'s father was alive until very recently. I can’t remember what happened to his mother, but IIRC, she was killed some time back.
Jim Gordon (father of Barbara Gordon, AKA Batgirl/Oracle) is still alive, last I checked. Although her mother died…before she was ever introduced.
The current Wonder Girl’s mother is still around. I don’t know about her father.
Impulse has only seen his mother once since coming to the 21st century. She may as well be dead - even if she even exists any more in the new 31st century. His father was dead before he was sent back.
Superboy never had real parents (being cloned from Superman and Lex Luthor*), but as I said, he’s being raised by the Kents (as their nephew).
Stargirl/Star Spangled Kid’s mother is alive, as is her stepfather (assuming the current JSA storyline goes well for her), although I’m not sure if her parents are divorced, or if her father’s dead. She has a younger half-brother.
Wonder Woman’s mother only died (relatively) recently - a year or two ago, real time, IIRC. Her father would be thousands of years dead.
Some more complicated ones (as if some of those didn’t get complex enough):
Jade and Obsidion are the children of the Golden Age Green Lantern (Alan Scott), who’s still alive. I’m not sure on their mother’s status. She left Alan before the children were born, then gave them up for adoption. I think Jade’s adoptive parents (the Haydens) are still alive, and she has a standard independant young adult/parent relationship with them, and she has someting of a relationship with her father. Obsidian killed his adoptive father. I don’t know the status of his adoptive mother. Given his being crazy and evil, any relationship he has with Alan would be strained.
David Knight, the second-to-last Starman’s father and younger brother were both alive when he was killed. His mother had died well before this. His father, Ted, was still alive for a while after Jack (the younger brother) took over. He was eventually murdered, but I don’t think that effected Jack’s attitude towards his carreer as a superhero one way or another. Getting married and having a child, did cause him to retire, though, and he started as a hero in order to avenge David.
Connor Hawk (Green Arrow II)'s father, Oliver Queen (Green Arrow I) is alive. But he wasn’t for a time. Since coming back to life, he’s developed a very close relationship with Connor, though. (He’d left Connor’s mother soon after Connor’s birth.) If Connor’s mother is alive, he isn’t shown to have a substantive relationship with her. At least not in the current series, I haven’t read the one he starred in.
Ollie’s also a father figure to Roy Harper and Mia Dearden, Speedies I and II. Roy’s an orphan, Mia’s a runaway.
(* We don’t need to get into the full story of Superboy’s cloning. It gets…weird.)