Zeus from classical Greek mythology deserves mention. Being the literal father of most Gods and thus ancestor of scores of heroes and demigods fully fills in for the Grandpa part, and you can't get more Badass than the god most frequently associated with the Bolt of Divine Retribution.
Belgarath (whose nickname is "The Eternal Man") from The Belgariad. He is seven thousand years old, generally accepted as the most powerful sorcerer in the world, and has about three and a half thousand years worth of descendants whom he calls "Grandsons". To add to it, Belgarath likes drinking, thieving, wenching, and has a surprisingly young body for a man who appears to be at least in his seventies.
Doroga also qualifies, although he's rarely physically underestimated on account of being incredibly buff. Not only can he accurately throw a coffin-sized chunk of solid rock, he's bonded to Walker, who at one point smashed a hole in a wall made of bedrock.
Another Eddings example: Preceptor Abriel of the Cyrinic Knights from The Elenium/The Tamuli. Near seventy, having been a knight for at least fifty of those years, eventually died in an attempt to charge Klael.
Lucifer in Dora Wilk Series. During a rebellion in Hell he almost single-handedly stops entire rebels' army. Justified in that he's ageless fallen archangel and looks forty despite being forty thousand.
Discworld has almost as many Badass Grandpas as it has younger badasses.
Cohen the Barbarian is a barbarian hero who is over 80 when he's introduced and he has survived over 60 years of fighting monsters and everything the gods can throw at him. He has a set of false teeth made from the teeth of a Troll. Trolls are made of rock and their teeth are made of diamonds. The books take the variation of 'A barbarian hero who gets to be that old is a very good barbarian hero indeed'. This is demonstrated when the Silver Horde (all seven of them) conquer the whole of the Counterweight Continent. The scene where they meet a dojo full of ninjas aptly demonstrates their awesomeness.
Six Beneficent Winds suddenly remembered, as a child, playing Shibo Yangcong-san with his grandfather. The old man always won. No matter how carefully he’d assembled his strategy, he'd find Grandfather would place a tile quite innocently right in the crucial place just before he could make his big move. The ancestor had spent his whole life playing shibo. The fight was just like that. "Oh, my," he said. "That's right," said Mr. Saveloy. "They've had a lifetime's experience of not dying. They've become very good at it."
In Thief of Time, young History Monks at their isolated mountain temple headquarters are taught Rule One (of at least Nineteen): "Do not act incautiously when confronting little bald wrinkly smiling men" and, in case this rule is forgotten, Rule Nineteen exists ("Never forget Rule One"). The reason these rules exist is because of one single History Monk, Lu-Tze. In fact, not only can he get badass warrior monks to wet themselves mid-punch simply by revealing his name, but he's also the reason why Ankh-Morpork's underworld has learned the value of Rule One as well!
Quite a few of the staff at the Unseen University qualify, but the best example would be ArchChancellor Mustrum Ridcully, who sleeps with a pair of crossbows and single-handedly ended a tradition wherein advancement in the wizarding hierarchy was performed via assassination (also known as the Dead Mens' Pointy Shoes rule) by virtue of being unkillable.
As of Night Watch, it's established that Vetinari and Vimes are both in their late forties. The novel also confirms that they are the only two people alive who have been taken off the Assassin Guild's register: they're so badass at their respective roles that the Assassin's Guild views their deaths as a catestrophic disaster for the city and therefore have banned contracts being put on their lives. So, not only do their enemies live in terror of them, but they're not allowed to be officially assassinated either!
Vimes also makes a habit of thoroughly boobytrapping his house against would-be assassins. Not one of them has gotten through, which helped the decision to take him off the list and definitely cemented his role as an object lesson for cocky assassination students.
TechnicallyDeath is one of these because he adopted a human girl, Ysabell, who gave birth to Susan who is almost as badass as her grandfather. Death takes on an entire army of Auditors during the Apocalypse during Thief of Time This is badass in itself, but even more so when Death actually used a loophole to attack them (the true villains). To wit: Nowhere does it say to whom we must ride out against. In Reaper Man where he was forcibly retired and in a semi-indestructible body he rescued a child from a burning building, defying fate and ended up killing the New Death with a scythe sharpened by his anger. He blackmailed the multiverse into letting the main characters of Soul Music live... really, any moment where Death appears show him as a badass. Even while masquerading as the Discworld equivalent of Father Christmas!
Also, Sgt Jackrum from Monstrous Regiment. Having been in the Borogravian army for sixt... a very long time and not dying makes you a prime example, even though he's not a grandpa.
Gandalf the White. Since he is an Ainu he is literally older than the universe. After coming "back from the dead" (he was sent back, because his job wasn't done — very much hinted at in the book and by Word of God to have been by Eru Ilúvatar aka God), he is granted an even greater use of his power — specifically, it's estimated that he was allowed to use about a third of his full strength as "the White", and was still able to take down a Balrog with his old strength.
Théoden also qualifies, being a seventy-one-year-old king of a proud warrior race. He defended his realm's borders his whole life and led his army in several wars during the book. It is told that in his last cavalry charge he even seemed one of the gods.
Aragorn is pretty obviously a badass. He's also (just barely) old enough to be Théoden's father; he was in his mid-to-late teens when Théoden was born. Of course, he's Dunedain, and due to Elvish (and Maia) elements in their ancestry they live longer than most men do; by the time he finally died he was over 200 years old.
Albus Dumbledore in Harry Potter. Although he was acknowledged to be the greatest wizard of all time since practically the beginning, so his magical abilities didn't came as a surprise; it's the raw badassitude he shows from the end of the fourth book onward.
By the same token, Hagrid, a half-giant and three years Voldy's junior.
Neville's grandma, Augusta, is a badass grandma herself, especially in the 7th book when she was able to fend off Dawlish (who was sent by the Death Eaters to go after her and take her hostage in order to blackmail Neville for standing up to the Carrows) all by herself; subsequently, she went on the run unscathed. The Death Eaters clearly underestimated her; lesson learned: never, EVER mess with Augusta Longbottom.
Another notable badass grandma from the Potterverse is Minerva McGonagall. She's a strict, but fair and effective teacher, and at the same time she has her many moments of badassery herself. Each of them were shown from the 5th book onwards. And hey, she survived four Stunning Spells to the chest in the 5th book — something that was not expected for someone of her age, as noted by Madam Pomfrey.
An age of seventy doesn't really mean as much to him, however. That would be more like an age of forty, tops, due to the Howard Foundation thing.
And Lazarus Long's first known appearance is at over 200. It's implied his lifetime is so long he may never die, and is badass enough to be a master at every profession including Piracy. He wears a kilt to have better access to his weapons at all times.
Ser Barristan "the Bold" Selmy is probably the best example. The Lord Commander of the Kingsguard, Selmy is still the second toughest knight in the realm at the age of 63. When he's kicked out of his post for advanced age, an unprecedented insult, he travels halfway across the world in the guise of "Whitebeard," an old squire. His badass chops with a staff betray his identity, however, and he eventually offers his services to a rebel queen. At the queen's court, some courtiers call him "Barristan the Old" and "Ser Grandfather," but he's still got enough spunk to train a new crop of knights and take down a pitfighting champion.
At the age of somewhere between 54 and 57, Ser Brynden "Blackfish" Tully serves as commander of the scouts in Robb Stark's campaign and is instruemental in several of the young king's victories. He later goes on to hold Riverrun against a siege by the Lannisters and the Freys. When he is finally convinced to give in to the besieging army, he has his nephew raise a gate leading out into a river and swims away in the night, escaping from his would-be captors.
Lord "Bronze" Yohn Royce is probably one of the best fighters in the Vale despite his old age. He's described as being as tall as the Hound (Roughly 6' 7") and looks strong enough to break lesser men in two. He's also mentioned to have hammered protagonist Eddard Stark and his master-at-arms Ser Rodrik into the ground with a sparring sword.
Amelia Peabody and her husband Radcliffe Emerson are Badass Grandparents in development. They are detective archeologists in a mystery series by Elizabeth Peters, and started the series at thirty-something. They are now actual grandparents but just as formidable as ever. Their major disqualification is that they aren't cryptic enough about it. Having been badass archaeologist detectives in Egypt for at least thirty years, their badassery is well-known to the locals. Also, Emerson at sixty-something is still a roaring bull of a man, only rendered more distinguished-looking (at least in Amelia's eyes) by the streaks of gray at his temples.
In David Gemmell's Drenai saga, Druss the Legend. Half a million Mongol Mooks are attacking a fortress held by nine thousand raw recruits. The only thing they're scared of is a fat arthritic 60-year-old man with an axe and an attitude.
In Sandy Mitchell's novels, Ciaphas Cain, HERO OF THE IMPERIUM, manages to retain his (in his own opinion, undeserved) badass status well into his ostensible retirement in Cain's Last Stand, going so far as to defeat Warmaster Varan in personal combat. On live, planet-wide pictcast.
Same can be said for Commisar Yarrick. At least a hundred years old he keeps coming out of retirement to fight the orks on Armageddon, and will probably keep fighting until he and Gazghul Thraka kill each other. The orks think he's immortal.
Dirk Pitt and Kurt Austin of their respective adventures are in their fifties in their latest books and yet they still get to kick serious ass and save the world.
David Weber has Wencit of Rum. The only living White Wizard and Wild Wizard. He's several thousands of years old and the one person upholding the rules of White Wizardry. He also is a Person of Mass Destruction, controlling the Strafing Spells that will coat an entire continent with Flames when he wills it. He also may be a god.
Elsewhere in the Weber bibliography, the existence of the drug Prolong in the Honor Harrington setting means that physical infirmities from old age are effectively no longer a bar to maintaining badassitude decades into the future.
In the Star TrekExpanded Universe Millennium trilogy, Picard is a 95 year old Admiral in poor health and well into the process of going senile. But when three Romulan assassins armed with disruptors attack him, he kills them all with a bat'leth. Naked, because he was in the shower when they attacked.
In one of the other expanded universe novels (written after Millennium, at a time when the novels had begun to be combined into a cohesive whole), the point is made that one of the benefits of an ever-lengthening lifespan is the increasing number of active centenarians — Picard is most certainly not alone in the badass 'old enough to be a grandpa' category.
In the Star Wars Expanded Universe, Luke Skywalker has gotten well along in years, but shows little sign of this other than mellowing out. He is still considered the strongest Jedi to have ever lived and perhaps the best lightsaber duelist as well. Toward the end of the last lengthy series, Luke pins Jacen Solo, also known as Darth Caedus, to a wall using Force Telekinesis with what essentially amounts to a shrug while he proceeds to calmly ask questions and inspect the room.
At about Luke's age we have Wedge Antilles. He was quite respectably awesome in the X-Wing Series, but at the end of it, in Starfighters of Adumar, he made a pivotal decision that doing the right thing was more important than duty, and from that point on, any time that Aaron Allston wrote him Wedge was unbelievably awesome. He became more picky about who he obeyed and why, blunter, more willing to screw the rules to preserve lives, tighter with his family and friends — and his tactics became outstandingly unorthodox. And his reflexes, if anything, sped up. Not only was he an outstandingly impressive pilot, but also one who had a fine grasp on strategy, tactics, and political ramifications, and who was a Reasonable Authority Figure of the highest caliber, who could sort of speed up his thinking to make complicated decisions within seconds.
By Legacy of the Force, when the Corellian military kicked him out for being too moral to support tactics like the assassination of neutral leaders, a sixty-year-old Wedge was given the choice to publicly hand over his position, swallowing his pride to do so, or just go off. He was able to examine the choice, realize that both were bad in different ways, and decide on the one which would hurt the fewest people in a quarter of a second. After that, just outside of the room he slumped in shock but was able to pull himself together as he realized that someone was going to try to assassinate him — yes, the idea that people were going to try to kill him made him relax, and by the time he left the building he was able to give the guards a smile "like he was a rancor and they were made of meat".
Why haven't we mentioned the literal Badass Grandpa in the Star Wars EU? After spending the past 71 years seeing the beginning of the Clone Wars, leading to the end of the Republic, the rise of the Empire, the subsequent fall and the rise of the New Republic, Boba Fett is a literal Badass Grandpa. His granddaughter is as badass as he is, surviving being tortured and crippled by Jacen Solo/Darth Cadeaus, Fett is the leader of the Mandalorians until Cadeaus releases a toxin that would kill anyone with Fett genetics, wherein he passed the leadership to his second-in-command and one of his only friends, issued a father-like warning to Mirta's future husband — "You break her heart, I'll break your legs" — and proved he is still a badass by tricking Jaina into letting her guard down around him and knocking her on her ass. Boba Fett, 71 years old and still proving to be the baddest of the badasses.
Basically, any member of the original cast who is still alive is a Badass Grandpa by this point. Some characters introduced in the '90s also qualify.
Snow Crash: Uncle Enzo, who is head of the Mafia as well as an ex-special forces soldier. He manages to fight off Raven with a straight razor.
Papa O'Neal from John Ringo's Legacy of the Aldenata may not perhaps as physically old as some mentioned on this page, he is a grandpa, literally, and is (or was, until the end of The Honor of the Clan) the head of a Badass Family, after having served in The Vietnam War and later as a mercenary in various hotspots around the world.
A malevolent example would be Dracula, who was of course Vlad the Impaler several hundred years ago and who (unsurprisingly) has white hair when we first meet him in the book before we discover him drinking blood.
The old blind gardener from World War Z. We know his age because his blindness is from the bombing of Nagasaki during World War Two, and the story takes place around 2006. When he hears of the zombie attacks and pending evacuations, he runs away into the forests so nobody has to worry about him. There, armed with his digging stick, he tracks and kills thousands of zombies with his hearing alone. And cremates the bodies and prays for them. Later he encounters the sorely-out-of-place Otaku and trains him in combat, and by the end of the book they're training more Japanese survivors to battle the zombies.
Any old wizard from The Dresden Files. Wizards only get more powerful with age and after a couple hundred years (or more) they are extremely powerful.
The Senior Council deserves special mention here. Ebenezar McCoy, their youngest and weakest member, pulled a satellite out of orbit to get revenge on Duke Paolo Ortego, he's also Harry Dresden's second mentor and literal grandpa. A couple steps up the seniority chain, we have Listens-to-Wind, who once sent a horrifically evildemigod off crying. And their oldest, most powerful member? He held off the entire Red Courtand the Outsiders they'd summoned with a single impromptu ward.
Roland Deschain is by far the oldest member of his ka-tet, even when one takes into account the differences in time between Mid-World and Earth, but he is also by far the most badass.
Moses and Joshua from The Bible lived to be 120 and 110 respectively, leading the Israelite people in their advanced age.
A companion of Joshua, Caleb, lived through 40 years of wandering in the desert and the entire campaign to take the Holy Land. And what did he ask for his reward after these long years of service? He picked to live on a mountain filled with giants and brigands, near the city of Debir. Just so he could eradicate the city by himself.
23. From there Elisha went up to Bethel. As he was walking along the road, some youths came out of the town and jeered at him. "Go on up, you baldhead!" they said. "Go on up, you baldhead!"
24. He turned around, looked at them and called down a curse on them in the name of the Lord. Then two bears came out of the woods and mauled forty-two of the youths.
25. And he went on to Mount Carmel and from there returned to Samaria. (NIV)
In the Andrew Vachss Burke book Strega, Burke briefly passes by an old black man who, after getting knocked down by a punk, proceeds to get up and school him like the retired boxer he probably was.
Martin Silenus from the Hyperion Cantos surgically modified himself to become a satyr at one point just to deflower as many females as possible. His vocabulary once dropped to a slight variation of the Seven Dirty Words. He's the only survivor of a Shrike attack on the city of Keats on Hyperion. Later (read: At the age of 700+), he got impaled on the Shrike's Tree of Pain. He died at the age of 1000, staying alive only because he refuses to die anywhere apart from Earth, and only if the Pax, the church is destroyed completely. The only problem is that Earth is either completely destroyed or in the Magellan Clouds, hundreds of light years away. He succeeds, and is buried on Earth.
In Ender's Game, Mazer Rackham single-handedly wins the Second Invasion, then takes a fifty-year, near-lightspeed space trip only to come back and kick the crap out of a kid that has been specifically bred, raised and trained to be 100% badass.
The Wheel of Time has several examples. Gareth Bryne and Rhuarc are probably the best ones.
Don't forget Thom Merrilin. He says he's just a gleeman but that doesn't stop him from taking on a Myrdraal with nothing more than his daggers and surviving the encounter or from killing a king over a dead girlfriend and throwing an entire country into civil war in the process. And that's just his offscreen badassery...
Gorynel Desse in Melanie Rawn's The Ruins of Ambrai is an expert swordsman, fabulous with both escapes and magic, and arguably the only character the villains even consider a threat. It doesn't hurt that he's in charge of a secret resistance and has been on the run for as long as some of the other characters have been alive.
Gorm was slain by Hialmar, a chief of the Nemedian Aesir. He was a very old man, nearly a hundred years old.
In "The Shadow Kingdom" Kull holds a man in contempt for weakness, and his age does not excuse him, because Kull has seen older men fight.
Cassel's grandfather in Holly Black's Curse-Workers novels.
Edgar Rice Burroughs's heroes Tarzan and John Carter certainly qualify, by having a grandchild and being disobedient donkeys. John Carter certainly fits the trope starting his story with:"I am a very old man; how old I do not know."
Otsi from the Northland Series is 15+-year-old Hazel's great-grandfather, and boy can he kick arse.
Jakub Wędrowycz, between some 80 and 90 years old (depending on when a particular story is set) is as fit as a youngster, has an entire arsenal of weaponry of all kinds hidden around and under his house (and can use them very well) — enough perhaps to defeat an entire army, and faces demons and psychopathic killers without the slightest hint of fear. And nearly all the old people in his village embody this trope to a similar extent.
Tadeo Kurita, in Carnifex, is over 90 years old, but still as ready to fight for the Dos Lindas, losing his life in the process.
See also Mr. Nguyen, helping the titular characters of The Amazon Legion in their guerrilla warfare campaign against the invaders even though he's probablynote his age is never really specified well into his seventies by that point.
Characters like Firestar, Cloudtail and Graystripe in Warrior Cats are grandpas, but still manage to kick large amounts of tail.
Benedict from The Chronicles of Amber has spent millennia studying combat and warfare. His godlike siblings have stated that if Benedict wanted the throne, they'd abandon their game of multiplayer Xanatos Speed Chess and let him have it.
The In Death series. Everyone who participated on some level in the Urban Wars Took a Level in Badass. Some of them took more than one level and retained it better.
Kit Carson of Time Scout found out he was a grandfather well after becoming a badass.
Sisterhood Series by Fern Michaels: Either Deconstructed or Subverted in the book Home Free. Harry Wong is training to become the number one martial artist in the world. To that end, he hires an old martial arts teacher who is at least 100 years old. Unfortunately, the old man does nothing except sit there and sleep...for 24 hours a day. Harry's friends, Jack and Bert pull some strings and have the old teacher/master carted out and bring in another old martial arts teacher who is at least 80 years and could wipe the floor with all three men. Shortly afterwards, the three men discover that the old teacher has up and died! In the end, Jack and Bert decide to be Harry's teachers.
Velisarios in Captain Corelli's Mandolin. At his last appearance, he's 87 years old and still has strength men a quarter of his age could only dream of.
Father James in Someone Else's War is not afraid to hide children in his church, no matter what the LRA does to him as a result.
Soo Kim McDivott, generally called "Teacher", in Emergence. A tenth-degree black belt, he intervened in a disturbance at a soda fountain. Four young toughs wound up being carted off to the hospital, and witnesses were certain Teacher hadn't moved a muscle. He's that fast, even in his 70s. Helps that he's a member of a Human Subspecies much stronger and faster than humans.
Pagan the Knight in Dragomirs Diary is initially portrayed as a weird old man in armour who needs a cane to walk. Get him into a scrap, though, and he'll cut your damned arm off.
Even well into his seventies, Mr. Walker is able to keep up his end of the deal in Islands of Rage and Hope when the climactic mission is threatened by zombie swarms, ensuring that every last Marine that went on the mission survives and returns.
In Hobgoblin, Conor and his brother, Fergus are over 80 years old, but are strong and tough due to years of hard manual labor.
Aaloon is over three thousand years old and he "beat manners" into the Number Two mercenary of the Dragon's Lair.
Tasio is known as the "Grandfather of Elves" because of his role in transforming Arin into the first elf. He is referred to and addressed as "grandfather" by the entire race, such as when they pray for his help against ordercrafters. Smiting ensues.
Bull: Used to be, when Dynamite knocked me on my backside I got right back up so he could hit me again. I don't have that will to win now.
Les Misérables: Jean Valjean is already kind of old when he escapes a prison work detail by jumping off a ship and faking his death. Another decade or two into the story, he's captured by Thenardier, burns himself to demonstrate his resistance to torture, then escapes when the police show up. Later on he's one of two survivors of the rebel group. He carries the other, injured and unconscious, on his back for hours through the Paris sewers, sometimes in muck so deep that he nearly drowns. Coming out of the sewers, he confronts a cop who's been trying to arrest him for years, and shatters the cop's entire belief system with the sheer magnitude of his goodness. And all so that his adopted daughter can be happy.
Achamian in The Judging Eye is about seventy and one of the most powerful magic users in his world, so powerful that he can fight dragons. And he also manages to father a child (bonus points for Squick — with a girl who believes she is his daughter).