Uncle Iroh. 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...
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!" While Toph is pretty close to his level, 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.
"Escape? I didn't escape! Everyone ELSE escaped!" (When he escaped imprisonment using only his chin and highhandedly retook an entire city in under eight minutes, on his own)
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.
Last is 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 PILES of 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, Admiral Zhao, Chief Hakoda (who's still only a clever Badass Normal in a world of superpowered martial artists) 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 to do so, 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".
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.
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 SolidSnake 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.
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 Plus One "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!
Transformers Animated 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. 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?
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.
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, Old Bruce and young Bruce team up. Old Bruce is so bad ass that young Batman HAS. TO. PLAY. GOOD. COP.
Henchman: I've told you everything I know.
Old Bruce: Everything?
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.
Immediately preceding the above example, young Batman, trying to get information on the Villain of the Week, holds the henchman 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 Henchman back onto rooftop and advances on the terrified Henchman holding his cane)This is how you interrogate someone. (Cue cut to the above exchange.)
Both examples can be seen here At approximately 3 minutes in.
Not actually an example, but the Beast With A Billion Backs four-episode Futurama special has Dr. Farnsworth describe Electromatter as "matter's Bad Ass grandma".
Hell, Farnsworth himself sometimes qualifies, when he stops acting like a Senile Old Loon and starts breaking out the Doomsday Devices.
Old Man Waterfall was a badass great-grandfather.
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 Bad Ass, 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.
Hudson and the Archmage of Gargoyles. Macbeth is certainly a Bad Ass. 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 Bad Ass 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. Grandpa's belt-fu, Rukas's being able to take on Huey, Stinkmeiner after his death (where even Satan had to give him his props) and Stinkmeiner's squad of friends 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.
Later, he takes on a horde of ravenous zombies with a baseball bat and his bare hands.