Avatar Roku was a powerful Avatar, master of all four elements, and fought a master firebender (Fire Lord Sozin) while in his 60s.
Uncle Iroh really takes the cake and then robs the whole damn bakery. For most of the series, Iroh seems an overweight, over-the-hill, past-his-prime wise man who would rather spend his days sipping tea, playing music and Pai-Sho, and generally forgetting about his past warrior-exploits. Early inklings of his badassness are shown, though, when, after being captured, not only does he manage to lead Zuko to him, but also nearly escape by himself; finally, with Zuko's help, he completely frees himself, and both fight off a band of half-a-dozen Earthbender soldiers with nothing but a pair of chains and martial skill (they didn't even have to Firebend...that would've been unfair).
Earthbender: Stay where you are! You're clearly outnumbered! Iroh: That's true...but you are clearly outmatched!
You also have his line when they were about to be captured by Azula in Season 2...
Iroh: [Picks up some tea and sips at it calmly, surrounded by soldiers] "Do you know why they call me the Dragon of the West?" [Stands up and breathes fire at his enemies]
Not to mention smoking his niece Azula, one of the most feared Firebenders in the world, in two seconds flat. Or tearing apart thick prison bars with his bare hands. Or using the Sozin's Comet powerup to blast through the functional equivalent of the Great Wall of China like it was tissue paper. Or leading a hand-picked team of four other Badass Grandpas to defeat an entire Fire Nation army, which leads to...
Special mention goes to the over 100-year-old King Bumi: "You thought I was just a frail old man, but I'm the most powerful Earthbender you'll ever see!" This is a man who can earthbend with his FACE, launch buildings made out of solid sandstone, and stack tanks on top of each other like dominoes. He was the world's greatest Earthbender for the majority of his life, with only Toph coming close (enough that it's a matter of some debate who was greater).
Next is Master Pakku, one of the greatest waterbenders in the world. Howzabout his waterspout when he's empowered by the full moon in "Siege of The North"? Or the waterfall/freeze it/unfreeze it thing for his party's grand entrance into Ba Sing Se?
Followed by Jeong Jeong, another Badass Grandpa firebender. He shows off his skills by creating walls of flames to destroy tanks while flying using jet feet.
Piandao, who looks like he's at least 50. He tends to use his sword as a cane (although that might just be for effect). He's also touted as the best swordmaster in Fire Nation (that is, the militaristic, imperialist, industrialized capital of the world) history. The Fire Nation sent 100 soldiers to arrest him for deserting the army, and they were all promptly defeated. It's unclear whether they were actually killed or just chased out by a 50-year-old man with a sword, but they still lost.
The previous five Badass Grandpas are members and leaders of the Order of the White Lotus, AKA Badass Grandpa: The Conspiracy. During the Grand Finale, they decide to retake Ba Sing Se, the largest city in the world, from the Fire Nation. They conquer the largest city in the world in less time than it takes to resolve Aang and Ozai's final battle.
And rounding out the bending arts is Monk Gyatso, Aang's long since dead teacher. The man's a pacifist, but when Aang finds his corpse a hundred years later, it immediately becomes apparent why he was the master. His corpse is sitting in a simple hut...surrounded by several Fire Nation soldier skeletons. Skeletons that, when alive, were likely powered by Sozin's comet.
The creators actually commented about this propensity in an episode commentary: There are either prodigious kids or badass grandpas; Martially exceptional young or middle aged adults are rare. The only major examples are Firelord Ozai and apparently Combustion Man. While there are plenty of young/middle-aged opponents who are relatively proficient fighters, they're just not up to snuff with the kids or the old badasses.
As of Book 3 of the sequel The Legend of Korra, former Firelord Zuko is around his late eighties and still going strong. He knows of the four convicts busting out and immediately makes a plan, gets to have a dragon as a steed, and holds his own against Zaheer and his gang. There's a reason why he's called "Lord Zuko".
Also, Bumi, Aang's son whose namesake is mentioned above. In this world, it's impressive enough that you manage to be in the fight with no Elemental Powers, since most major players have immense bending ability and their Mooks tend not to be slouches either, and the ones who aren't benders use mecha-tanks. Bumi may not control the ground beneath their feet, but he's every bit the 'mad genius' his namesake is. He loves to tell wild stories about his past battles that absolutely no one believes, but you realize they're Not Hyperbole when he manages to singlehandedly rescue the rest of the cast. Oh, and now he's an airbender.
Master Splinter of Teenage Mutant Ninja Turtles fame quickly comes to mind. Not only does he train otherwise normal mutant turtles to be freakin' ninjas, he also manages to kick his own fair share of ass on several occasions in the comic books and the television series. In most incarnations he's the only one able to go one on one with Shredder, who's consistently capable of going fighting off all four of the turtles on his own.
Sadly, at least in the 1980s series, his job was all too often to get captured or otherwise indisposed. That being said, he was the only character who could take Shredder in a fair fight.
The 2012 series sees Splinter kick butt a lot. The first time they fight Shredder, he waits until it's clear the Turtles can't take him on their own, then proceeds to beat him without any help (except for gravity, perhaps).
Also, later in the show they all go to a multidimensional fighting tournament, and the Turtles learn from a contest veteran that Splinter once won the whole thing...with a broken leg, no less.
One time, there was a villain doing the Body Surf who had taken over Master Splinter, but moved on earlier unbeknownst to the Turtles, who dogpile on Splinter...and two seconds later, are sent flying away by Splinter, who stands up, looking only mildly annoyed while asking them "What is the meaning of this?"
Several mooks who are dumb enough to try sneaking up on this ninja master often get one hit KO'ed by Splinter's cane without him even needing to look.
American Dragon: Jake Long. Despite his old age, Grandpa Lao will still take on his dragon form to fight side by side with his grandson on frequent missions. This is the opposite case in The Life and Times of Juniper Lee where Grandma Jasmine only assists Juniper Lee in extreme circumstances or when she is absent during a mission.
Nana Possible from Kim Possible. While only making a few appearances in the show, the two times she's been directly involved in one of Kim's adventures, she's shown remarkable martial skill for anyone of any age. In fact, Dr. Drakken revealed that, in her prime, her exploits apparently dwarfed even Kim's (in fairness to Kim, it's implied Nana's career was much longer than Kim's has been so far), and after he uses a mind-controlling transition on Nana, he has her fight Kim herself. Nana had one clean hit on Kim, but when Kim quickly ended the fight by shutting off the said transition. After everything is back to normal, we see Nana beat Kim in a sparring match, and the end.
Think that's badass? She was the first woman to complete the Navy's Underwater Demolitions Training program, the training Navy SEALS go through with a low success rate, complete with five days of sheer endless torture during Hell Week. Never, ever, mess with granny.
Max Tennyson in Ben 10 — the protagonist's literal Grandpa, a former Plumber. The fact he's voiced by the same guy who bossed Solid Snake around just puts the icing on the cake.
Atomic Betty's grandma Beatrix was a famous Galactic Guardian in her day, and still kicks butt as needed. Bakes great pies, too.
The Transformers features many. Primus, practically as old as the Universe is the friggin' creator-god of Transformers, and the size of a Planet, so he could take on anything! Landmine from Transformers Cybertron took out a super-sized Starscream; granted, he was the same size, but bear in mind he was built before Optimus. Vector Prime from the same continuity was the keeper of space and time! Just a little younger than Primus, he could use his transformer-scaled Claymore-sized mystical Infinity +1 Sword "Rhisling" which could teleport all the 'Cons into a black hole.
Ironhide is usually old, but he's tougher than any other 'bot on the Autobots, except maybe Omega Supreme, who's a friggin' spaceship for crying out loud!
And Omega Supreme ain't no spring chicken. Pretty much every continuity he appears in, he goes back a ways:
G1 Omega was one of the Sentinel Robots that worked on Cybertron during one of the Constructicons' origin stories. We eventually find that the Sentinels were originally used by the Quintessons when they ruled Cybertron: we don't get many exact dates, but to these guys a million years is nothing, and by their standards it's ancient times and we know only one guy who was there.
Energon Omega Surpreme was someone who went toe to toe with Unicron in what is, again, considered to be ancient times by those who think of a million years as nothing. (Mind you, some of those millions of years were spent in stasis lock until Dr. Jones found him, so it's hard to know how well he counts.) Naturally, he leaps right back into battle and becomes the Autobots' trump card.
Animated Omega Supreme is a hero from the war in a universe where the Forever War actually ended at some point and the main Decepticons are The Remnant. Not everyone knows that the ship is actually him; he sustained fatal damage and was deactivated, his body controlled by a non-sentient AI called Teletraan I. With Allspark energy, he as able to return to his true self and true badassery and unleashed a Curb-Stomp Battle on a whole mess of 'cons who are each alone a match for the entire main Autobot team. It was truly glorious.
Transformers Animated also has Ratchet, the old war veteran medic who can kick your ass and then put you back together again. Also known as the person who had the ball bearings to call out the Autobot Elite Guard on their unethical practices.
It could be argued that Brawn is this, but seeing as he was only on screen for a small part of the opening of one episode it's a little hard to tell how old he is. In that time he did rip out a chunk of the ground and nerly take out two Decepticons single handed. Oh, And did I mention he's tiny?
Animated Arcee, who was already fighting in the War during Ratchet's days as a young medic, counts as a Badass Grandma.
The Ratchet of Transformers Prime follows suit. His advice for dealing with a small army of undead robots? "I recommend dissection."
Kup is another triumphant example. Basically, the "old badass" portrayal of Ratchet in recent years? Fans who've been around since the beginning have been saying "since when does Kup turn into an ambulance?" whenever they see Animated or Prime Ratchet for the first time. Kicking aft and taking names while talking about how this reminds him of some other battle back in they day is how he rolls out.
And then, there's Alpha Trion. He too comes from the Quintesson days, and led the battle against them to free Cybertronians from their enslavers. Again, this is forever ago to alien robots who think nothing of your idea of "forever ago," and unlike some other names on this list, there's no sign he wasn't active for every day of it. He went on to become the leader of the Autobots back on Cybertron while Optimus Prime is on Earth. He eventually becomes one with Vector Sigma, the central computer that controls Cybertron (this was before the idea of Primus ever came along. Arc Welding to connect Vector Sigma to Primus has happened and isn't exactly the same in every retelling, but basically, Vector Sigma is to Primus as Animated Teletraan I is to Omega Supreme. That is what Alpha Trion is now one with!) and though this puts him in more of a "glowy mentor" state than a "direct buttkicking" state, really, think of what that means - God is napping, so Alpha Trion has his job for the time being. And before he was Vector Sigma, he was the only one who could give commands to it.
Bruce Wayne from Batman Beyond. A bat-shit Crazy-Prepared old man who can beat up street thugs with nothing more than his cane, and who can still beat supervillains as well (in fact, Terry has stated that Bruce was the only person who could beat his toughest foe, Inque). Subverted in the fact that Bruce is Terry's father, not his grandfather but now we're just playing with semantics. Made all the more awesome when the writers make him believably old — when he gets riled he needs a dose of his heart meds and a nap afterward, but of course that would be after he's laid the smack down on some unsuspecting chump.
In one episode of Justice League Unlimited, Old Bruce and young Bruce team up. Old Bruce is so bad ass that young Batman has to play good cop. Modern Batman is dangling a crook over the edge of a skyscraper:
Batman: Where's Cronos? My arm's getting tired.
Old Bruce: I can't believe I was ever that green. (throws the thug back onto the rooftop and looms into the camera, fingering his cane)This is how you interrogate someone. (Brief cut to black:)
Henchman: I've told you everything I know.
Henchman:' ...I wet my bed until I was 14.
Old Bruce: I'm losing my patience.
(Batman puts his hand on Old Bruce's shoulder, pulling him away from the perp)
Batman: I can't control my friend here much longer, you better give us something we can use.
The last surviving member of the Blackhawks in Justice League Unlimited. Has what looks like a modified (to have two heavy cannon) F-4 Phantom-II in his barn. Shoots down a robot-vulture (part of the subverted Blackhawk Island defences) that was giving Hawkgirl, Flash, and Fire serious trouble. Gets taken hostage by Lex Luthor, which is not so badass, but manages to get away and get back to disable the island self-destruct, which is.
In The Adventures of Sam & Max: Freelance Police episode "Christmas, Bloody Christmas", Sam's Granny Ruth is a former prison warden who manages to both spread holiday cheer at the prison where she used to work and thwart a prisoner's escape attempt.
Grampa Abe Simpson from The Simpsons is for the most part a crazy old man, but he showed he still had it in "The Flying Hellfish."
When he helped Bart in "Bart the General" that was pretty awesome too. It's quite sad that this this side of Abe is rarely shown, and nowadays is all but forgotten.
Phil in Hey Arnold!. How badass is he, you ask? In one episode he punched out a shark.
Hudson and the Archmage of Gargoyles. Macbeth is certainly a badass. His aging may have been magically done, but now he's one step removed from immortal due to said magic, and as such he's been alive for about 1,000 years.
Halcyon Renard manages to pull this off while riding around in a wheelchair. Said wheelchair has a laser gun built into the armrest, potent enough to knock out a full-grown gargoyle like Goliath.
After capturing Goliath and calling him out on the destruction of his last airship, he responds to Goliath's denials with "You sound like every whiny employee I ever fired!"
One More Thing...Uncle from Jackie Chan Adventures appears to be your typical elderly Chinese man obsessed with the cleanliness of his shop...but he's also the local expert on the mystic arts and no slouch in the martial arts, either. Not that he cares...if he had a choice in the matter, he'd rather just run his shop.
He gets even more badass in The Dog and Piggy Show, when powered up by an immortality/youthful energy talisman. Not so antique anymore...
Lucius Heinous VI on Jimmy Two-Shoes, if "Team X-treme Team" is anything to go on.
Papa Smurf in The Smurfs. He often saved the day and would often volunteer for dangerous physical tasks.
The nurse from The Thief and the Cobbler, beating up the thief when he tries to steal her bananas and attacked some of the banits. The witch in the ReCobbled version, swinging around the mountain like Tarzan.
Both Saladin and Hagen in Winx Club have shades of this. Hagen is the Smith of the Universe, willing to take on six Enchantix fairies and Saladin can stop massive burns as if they were simple campfires. He also is roughly equal in power to Faragonda and Griffin. Both of them were in the Company of Light.
Mr. Herbert from Family Guy fought possessed trees and Nazis to save Chris.
Peter's "father" Francis retired from one job, was hired at Peter's factory, and immediately worked circles around everyone. He was also on the Pope's road crew, punching out photographers and such.
Brother Blood from Teen Titans never has his age specified, though going by both his appearance and general personality he's unlikely to be younger than late middle-age. He's also probably the most individually powerful villain in the series barring Slade and Trigon.
Cotton Hill is in his mid 70's, and "Had his shins shot off by a Japan mans machine gun" but he's still easily capable of kicking the asses of men several decades his junior.
General Treister from The Venture Bros.; though he is a bit of a Cloud Cuckoolander (probably comes with the territory of running an ultra-secret espionage organization), he is undoubtedly badass.
Colonel Gentleman as well. Formerly in the RAF and MI-6, and based heavily on James Bond and Alan Quartermaine. He even gets Brock Samson to back down with a well placed cane strike.
Ruel from Wakfu. In fact he is hinted at being the strongest of the group.
Sheen must fight a karate champion on Jimmy Neutron and is trained by an old person. Sheen asks the trainer "Arent you a little bit old to be teaching karate"? so he beats up Sheen to show him.
Nearly every old person in The Boondocks. Robert and his belt-whip fighting style, Ruckus and his nunchaku skills, Stinkmeaner after his death (where even Satan had to give him his props), and the Hateocracy who are basically a badass grandparents trio.
Old Man:(Has Dan in a neck-lock) I learned this move on the (cough), on the beaches of Normandy.
Dan: Shooting out or shooting in?
Arthur Puppington is this in the Moral Orel prequel Beforel Orel. Especially when he stops Orel from stabbing Shapey.
Hank's dad from King of the Hill. He's Cotton Hill, and he killed fiddy men. Ever since he lost his shins to a Japanese machine gun in dubya dubya two, he spends most of his time smashing things and slapping rear - that is, when he's not getting his wife pregnant through "four layers of protection".
Buzz Lightyear of Star Command: Commander Nebula. In his youth, he was the Buzz Lightyear of his day, and he can still kick copious amounts of ass. That peg-leg of his? It's a blaster cannon.
Spider-Man: The Animated Series had an entire team of WWII-era superheroes who had fought alongside Captain America, and were able to give the Insidious Six a run for their money despite being over 70 and only having limited powers.
In Gravity Falls Grunkle Stan seems like just a crusty old Con Artist, but it's eventually revealed he took boxing lessons as a kid, and in "The Land Before Swine" he saves Mabel's pet pig by punching out a pterosaur.
In the season 2 premiere "Scaryoke", Grunkle Stan takes on a horde of ravenous zombies with a baseball bat and brass knuckles.
There is also Old Man McGucket, who despite being in his elder years can still singlehandedly build giant robots and take out a cult leader.
And then of course there is the Author of journals Stan's twin brother Ford, who is the same age as Stan and if anything even more Badass.
In the Batman: The Animated Series episode "Beware the Gray Ghost", Batman meets Simon Trent, the now elderly actor who played his childhood hero, the Gray Ghost. Despite insisting that he's just an actor, he ends up saving Batman's life twice, and even performs a Super Window Jump to tackle the villain.
Alfred is officially a Retired Badass as is a former British intelligence officer, and he shows in several episodes that he's still fit and capable of kicking some asses.
Rick Sanchez from Rick and Morty is an old Mad Scientist who is the most intelligent man on earth, having invented a number of gadgets including his trademark portal gun that allows him to travel between dimensions. He's also remarkably strong and agile for a sixty-year-old man and is also very protective of his grandkids. In "Close Rick-counters of the Rick Kind" he takes on a number of massive alien beasts in basic melee combat and kills many of them, and in the Season 3 premiere (which is an episode-long Crowning Moment of Awesome for him), he topples two intergalactic governments all by himself.
Star Wars Rebels has the clones. Thanks to Rapid Aging, Rex, Wolffe, and Gregor are biologically in their mid 50s, but still tactically brilliant, excellent shots, and far superior to the stormtroopers they're pitted against. In a more conventional example, Maul, who is in his 50s naturally but still slices apart Inquisitors, blinds Kanan, and easily manipulates the Jedi into doing his work for him.