Abraham Setrakian from The Strain. He has been pursuing the Master since first encountering him during World War II. He dispatches numerous vampires using his wolf`s head handled silver sword-cane well into his 80s.
Father Jack Hackett and Bishop Brennan from Father Ted.
Rodrik Cassel, who shrugs off a sword wound and defeats men half his age, such as in the fight to the Eyrie when he keeps up with Bronn despite being half his age. Clearly, his age cannot hold him back.
Jeor Mormont, the Lord Commander of the Night's Watch; and Tywin Lannister, one of the few men in the kingdom who can intimidate his grandson King Joffrey.
Ser Barristan Selmy might be the best example of all. In the first season, Ned states that he would be dead had they ever met in single combat during Robert's Rebellion. When he is discharged from the Kingsguard by Joffrey, he challenges the remaining other knights to dual him at once, confidently saying he would kill them all with ease. None of them move even a muscle. Finally shown in his last-stand before death as he cuts down about 20 Sons of the Harpy by himself while completely surrounded.
Jaime: Ser Barristan was an artist. An artist who only used red.
Rickard Karstark has reached his elderly years, but it hasn't stopped him from kicking ass in the War of Five Kings.
Whatever else he is, Craster's badassery is evidenced by In-UniverseMemetic Badass Qhorin Halfhand suggesting there's no shame in being beaten by such a "tough old goat" and his ability to hold his keep by himself in a culture where taking from others is a way of life.
Inspector Rex: Filippo Gori is not very active, but has a good physical condition and is willing to engage in active work. He eventually saves Rex and his owner at that time.
Teal'c himself who, despite looking young, was actually about 100 when the show began. Then, in the last episode he alone is aged 60 years on top of that. He still mopped floors with those who were dumb enough to cross him.
General George Hammond, despite being over 60, put on fatigues every now and again and blasted the crap out of bad guys. (see also General Jacob Carter, father of Colonel Sam Carter).
In Stargate Atlantis Major Sheppard is aged into an old man by the constantly feeding Wraith. Most people would literally wither and die. Major Sheppard ain't most people....
Lt. General Jack O'Neill, over 50 by now, a legend across the galaxy, and still a badass...
One random extra in the pilot, a man of unknown age but appearing to be at least sixty, who throws rocks at the Jaffa army, as well as manhandling some of them. Bear in mind that Jaffa are physically stronger than the average human in his prime, let alone an elderly human who'd just been sprung from a Goa'uld prison.
Earl Haraldson (played by Gabriel Byrne) is also no slouch. Having been described as a great warrior in his youth, he proves it when he faces the protagonist; Ragnar Lodbrok, in single combat. Despite his age, they're evenly matched. (though Ragnar has handicapped due to his leg and was barely healed from several life threatening wounds)
The First Doctor is a crotchety old man...who somehow outfought armed knights with just his cane and a sword-wielding assassin with a harp. The Second Doctor pretended to be a clown, yet was more than capable of taking out the strongest Yeti. And then there was the Third...who was a master of Venusian Aikido and was also capable of out-fighting two men in a sword fight at the same time, while wearing a horribly clunky suit of armor that offered little protection. The fact that the Doctor is probably over a millenium old and has / had a granddaughter makes him technically this trope even when he looks around 30 years old.
In his last appearance in the old series The Brigadier was getting into this territory as well, facing down the Destroyer of Worlds all by his lonesome with nothing but a revolver and silver bullets. And winning.
Wilfred Mott. Apart from using a paintball gun against a Dalek (it didn't work, but that takes balls), between the pistol and the laser turret, he becomes one of the biggest badasses in "The End of Time".
Don't forget he was the only person that stayed in London on Christmas in "Voyage of the Damned".
Captain Jack Harkness. He doesn't look it, but he has at least one grandson. or rather, had.
The War Doctor was the Doctor who fought and put an end to the Last Great Time War. He is played by John Hurt, who to date is the oldest actor to portray the Doctor.
At the end of his life the Eleventh Doctor, despite being in an incredibly aged body, becomes this when he uses his regeneration energy to destroy a Dalek Force. And of course at the end of this regeneration he's become a grey haired and grumpy Scot.
The pirate Gaptooth from The Smugglers was in his seventies. In the seventeenth century, no less.
An episode of Kamen Rider Double featured a Dopant who can affect people's age. After he ages Shotaro into an old man, Double is unable to form since one half is having trouble just staying awake through the fight. Then Old Man Sho decides to take on Old by himself, including his trademark 'Count up your sins!' catchphrase and pose. He's not very effective but damn he's got guts.
Captain James T. Kirk was busting bad guy asses well into his 50s and then came out of retirement to help Picard take down Tolian Soran.
And for "retirement", see "death."
Admiral Kathryn Janeway (the older, gray-haired version of Capt. Janeway) who defied the Prime Directive, the Temporal Prime Directive, lied to Starfleet, and swindled a Klingon and gave him the finger. All to bring Voyager home earlier. Even people who don't like Captain Janeway love the Admiral.
The Klingon captains Kirk butted heads with (Koloth, Kang, and Kor) turned up well past the century mark and still ready to kick serious ass in Deep Space Nine.
Even Odo has learned not to bother arguing with Klingons when they're bragging
Odo: How did you get in here?
Koloth: I am Koloth
Odo: That doesn't answer my question
Koloth: Yes it does.
Heroes has Daniel Linderman, Maury Parkman, Angela Petrelli, and the granddaddy of all badasses Arthur Petrelli. (See also Hiro's father Kaito Nakamura, whose badassery is increased by being played by George Takei).
Mrs. Westen from Burn Notice manages to break a suspect by just sitting down and explaining how things will end if he refuses to talk. And this was after Sam and Fiona failed in interrogating him. All Madeline did was offer him a cigarette and talk about how he wouldn't have to worry about cancer. In another situation, Madeline also directly resisted the FBI by sending them on a wild goose chase while warning Mike about their investigation. They arrested her and she still didn't tell them anything.
Midsomer Murders episode "Sins of Commission" has a female version, Camilla Crofton. She killed them all. In self-defence, as they were trying to off her. It's quite possibly one of the most awesome "how they did it" flashback sequences ever.
Samurai Sentai Shinkenger: Mess with the Samurai Sentai authorized by the Providence, you may just get to face their Badass BikerStern Teacher head of the household servants, Kusakabe Hikoma. Lovingly known as Jii, he keeps the Samurai-tachi fed, trains them in the use of their powers... and will go hand to hand with the demonic mooks for his Lord if he needs to.
The Zen Master from Fist Of Zen. He has been shown, among other things, demolishing a nuclear reactor by sneezing. And then putting it back together through sheer force of will.
Battlestar Galactica: Admiral William Adama. In season 4, during a mutiny of Galactica's crew, the Admiral can be seen dual-wielding assault rifles for the better part of the conflict. He's also 73 by the end of the series.
Arguably Battlestar Galactica as well, akin to a WW2 era aircraft carrier taking on a Nimitz-class aircraft carrier and winning
Dr Quentin of the Spy Game television series, played by Patrick MacNee as a semi-regular. His first appearance has him playing a sedate round of golf with an old espionage buddy (played by Mission: Impossible's Peter Lupus), when they're suddenly confronted by a much larger squad of young toughs. A fight ensues. Guess which side wins?
Some might argue that Ducky,who has chased down kids who egg his van and had Fornell in a respectable (and accurate) headlock, shows signs of Badassery.
No longer arguable after he and a former girlfriend were taken hostage by [[spoiler:his childhood friend's murderer], and Ducky responded by slicing the captor's brachial artery with a scalpel, killing him.
Jackson Gibbs is also a good example of this, chasing off Paloma Reynosa and Alejandro Hernandez when they come to attack him with just his old rifle.
The JAG episode "Yesterday's Heroes" has three retired underwater demolition divers (one played by Ernest Borgnine) in Florida avenging on a South American drug dealer who'd hurt one of their grandchildren.
Jason Gideon of Criminal Minds, who has shown himself capable of outmaneuvering a man who had him at shotgun point, both mentally and physically. Dave Rossi as well.
Angela's father, Billy Gibbons of ZZ Top fame, playing himself. Angela's middle name in the show, "Pearly Gates," is a reference to Gibbons's favorite guitar.
Let's not forget Bones's father. When a corrupt cop posed a threat to his son and daughter he stabbed him, gutted him and burned him at the stake. He did this to two people in that episode, in fact. Now, that's badass. And during the Season 7 finale, it's revealed he used his underground contacts to help his daughter and granddaughter get off the grid for a while when they're being targeted by a serial killer.
Mike Ehrmantraut in Breaking Bad. Loves spending time with his granddaughter. Capable of taking out a small building full of Mexican Cartel enforcers.
Gaius on Merlin. Probably Uther, too. Not grandpas, but still old enough to be and definitely both have moments of badassery.
CSI's Jim Brass and maybe even Grissom. In later seasons, D.B.Rusell has a few moments, especially when his granddaughter was kidnapped.
M*A*S*H: ** Colonel Sherman Potter in M.A.S.H. is old enough to recall WWI but can keep up with his younger medical collegues on operating table; further he runs the hospital with warmth coupled with a do-it-now voice of command that makes even Hawkeye tow the mark.
Clay Morrow is still leading an outlaw biker gang at an age where his adopted son has a kid. His hands are getting brittle, but otherwise he's still able to mix it up with the rest of the gang.
Despite being an Irish Priest in his 60s, Father Ashby is a high-ranking leader of the Real IRA. When Badass Biker Jackson Teller rushes him in a rage, Ashby simply tosses him to the ground.
Piney is one of the original founders of the Sons, and his own kid (Opie) is in the club as well. He's not entirely hearty and hale, and does have to carry around an oxygen tank for his emphysema... which he's used to beat the crap out of someone on more than one occasion.
Hooch, The Listener, in Criminal Justice, runs with this. As a Parental Surrogate AND Papa Wolf to Ben, he takes out Milroy in one punch despite the thug being a lot younger and apparently in much better shape, then later nearly kills Freddy so he'll give him the name of the man really responsible for Melanie Loyd's death and clear Ben's name, knowing Freddy's retaliation, having his thugs inject him with a lethal dose of heroine to make it look like suicide, will know doubt follow, and takes it without fear. For an old dude who doesn't appear particularly tough, that's pretty impressive.
Howard Stackhouse, a United States Senator in The West Wing, out of pure desperation to attach an appropriation for autistic children to a bill, that has been closed and is about to pass to a vote, seeing himself devoid of political leverage to reopen the bill, at the ripe old age of 78 starts a NINE HOUR MONOLOGUE, wherein he is not allowed to stop speaking, eat, drink, sit or even LEAN ON SOMETHING. The staff of the White House is able to determine, that Stackhouse is in fact doing this for his autistic grandkid, and finally muster a kind of "rescue operation" where other Grandpas in the Senate alleviate Stackhouse by posing questions pertinent to autism and are together able to push the vote so far back as to reopen the bill for appropriations. Maybe not the most colourful example of this trope, but as Jed Bartlet puts it: "Don't ever, EVER underestimate the will of a grandfather. We're mad men. We don't give a damn. We got here before you and they'll be here after. We'll make enemies, we'll break laws, we'll break bones, but you will not mess with the grandchildren!"
Rupert Giles from Buffy the Vampire Slayer initially a bookish man in his mid 40's. By the series end he is in his 50's and while he isn't a parent or a grandparent he has gone toe to toe with innumerable vampires, fought demons (both the regular hybrids, an insane cyborg and a full fledged one) fought a god, stopped a witch from destroying the world (admittedly he lost that fight but she was coked up on more magic than was safe) and helped stop the end of the world. About a dozen times.
Samuel Campbell from Supernatural is quite the badass and is Sam and Dean's grandfather. The complications of time travel (he died at age 42 in 1973, and was brought back to life in the present at the same age) mean that he is too young to be their grandfather normally, but at least he's an older man to them and old enough to be their father.
Doc from Z Nation may act like an old hippy most of the time, but he can make running head shots more often than not and beat younger, better armed survivors to death. With letter a letter opener he found during an out-of-body experience while said survivor was strangling him.