In the Flashpoint storyline Batman's father, Dr. Thomas Wayne becomes Batman after Bruce is are killed in the mugging. He's as good as Bruce at the job, but he's probably pushing 60 AT LEAST.
Col. Jacob Kane, Kate Kane's father, was a decorated veteran involved in many Special Forces operations. He also taught Kate how to box when she was young, and years later organized her training to become Batwoman.
The assassin Deadshot aka Floyd Lawton, on-and-off member of the Suicide Squad (and one of the few good enough to survive multiple stints on it) and member of the Secret Six (pre-Flashpoint). In one storyline he discovered that he might have fathered a daughter. When he visits the mother Michelle (a former prostitute and junkie who cleaned herself up for her daughter's sake) he sees his daughter for the first time, an adorable little four year old girl named Zoe. He wages a one-man war against the three crime families fighting over their neighborhood just so Michelle and Zoe can have a better life. He wins too. He later finds out he has another kid to boot.
Similarly, Deathstroke, Slade Wilson, father of three, who took up a personal vendetta against the Teen Titans when one of his sons died fighting them. His other children, Rose and Joseph, meanwhile, instead joined the group. He's an action dad, but a terrible father non-the-less.
Wally West also has twins, Jai and Iris West, who both have access to the Speed Force in different ways.
James Jesse has a son named Billy Hong, however he only had a handful of appearances before never being mentioned again.
Mark Mardon has a son named Josh Jackam, who has lightning based meta powers. Josh was originally thought to be Wally's child, as the lightning was thought to be Speed Force, however it was eventually revealed that Mardon had had a one night stand with cop Julie Jackam.
Digger Harkness has a son named Owen Mercer. Digger Harkness had ended up in the 30th century, where he met and had a child with Meloni Thawne. How and why Boomerang and Owen made it back to the present is currently unknown. Owen went on to be a Legacy Character after Digger's death in Identity Crisis (2004). Owen would semi-reform and join Nightwing's Outsiders, before ultimately following in his father's footsteps and joining the Suicide Squad.
Roy Harper, AKA Speedy/Red Arrow/Arsenal, who fathered a daughter with the super-villainess Cheshire, one who he was VERY protective of. When they disgustingly killed her off, Roy went a bit nuts.
Scandal Savage and Bane of Secret Six have something of a father-daughter relationship, with Scandal's biological father being... well, Vandal Savage and Bane being a Genius Bruiser when not on his venom, and it seems the one surefire way to get Bane to use said venom again is to put Scandal in danger, at which point anyone who happens to be in the way gets to experience what the Batman went through in Knightfall — that is, a broken back.
A rather twisted example would be Sinestro. Harm his daughter, Soranik Natu, and you will have the wrath of the entire Sinestro Corps bearing down on you and your entire planet, as the Weaponer of Qward learned. Being Sinestro, this happens after he lets his daughter's boyfriend, Kyle Rayner, fail in a rescue attempt first just to show her how unworthy he is.
Superman obviously falls under this trope. Especially mess with Conner, his cousin Kara -Supergirl-, his cousin from an Alternate UniversePower Girl or his adopted son Chris and you'll be under a worse ass-beating than usual from Supes. As of Convergence, Superman actually has a biological son, Jonathan Samuel Kent. Threaten Jon at your own risk.
Jeremiah Danvers is Supergirl's foster father in Supergirl (Rebirth). He's a veteran Government agent trained to neutralize super-powerful alien threats.
Even villains can fall under this trope. When Marvin and Wendy suffer their utterly ridiculous, cruel, and pointless death and maiming respectively at the jaws of a demonic Wonder Dog while working with the Teen Titans, their father The Calculator is somewhat understandably pissed. Being a villain, he acts as a very dark Papa Wolf. His vengeful scheming has already claimed the life of Eddie Bloomberg aka Kid Devil. He's even gone so far as to search for the Anti-Life Equation in the hopes that it could restore Wendy's ability to walk. It didn't work out.
Wonder Woman (1942): Steve Trevor remains an active government agent after he and Diana have a daughter together, though he's essentially on call and spends a lot of time with Lyta.
Ares has several children, and usually does a better job of trying to look out for them than any other Olympian does for theirs, and is an incredibly active super villain.
Live-Action TV
Jonathan Kent on Smallville was actually pretty legendary in this regard. One memorable scene was when Lionel tried to blackmail him again, or he'll expose Clark's secret to the world. He chose to beat seven shades of crap out of Lionel, nearly killing him, until he was struck with a heart attack, and died. He sacrificed his life to protect his adopted son.
Granted, the situation was not quite what he thought it was (Lionel was actually on the way to a Heel–Face Turn at this time, and himself took Clark's secret to the grave 2 Seasons later), but given Jonathan's history with the Luthor family, his overreaction is understandable (and Lionel even admitted his fault in Jonathan's death).
To drive that point even further, the villain was his own brother, Orm. And Aquaman didn't give a single thought about kicking his ass and letting him die.
