Shigekuni Yamamoto-Genryuusai from Bleach. The Older Immortal Badass Grandpa who is a formidable fighter after being in his position for a thousand years - and boasts about it. The head of a Badass Army, and known to be the mentor of two secondary characters, but not the main character, who gets very different people.
Ryuken in Fist of the North Star, the previous Hokuto Shin-Ken master who trained Kenshiro and his adopted brothers. Also, Ryuken's old rival for the succession, Koryu, as well as the Hokuto Ryu-Ken master Jukei, both qualify.
Netero from Hunter × Hunter, still one of the most powerful people on the planet despite being over 110 years old. Not a sensei anymore, and he's still active (though rarely involved in fights) as the head of the Hunter Association, but he fits the trope otherwise.
Subverted in Mahou Sensei Negima!, where the Old Master- who comes complete with mysteriousness, tea drinking, and repeated comments about today's youth- looks like a ten year old girl, has a crush on the main character, insists she is utterly evil, and makes at least token attempts to turn her students to The Dark Side whenever the topic of conversation veers anywhere near a decent opening. Well, that and an occasional detour into vamp territory, which generally fails spectacularly due to the fact that her main pupil/object of her affectionsisten. Oh, and it is not just magic, for she has been studying Aikijujutsu for the past century and probably learned it from the fellow who originated same.
The first words out of anyone's mouth when they face down Andrei Rublev on IGPX's race tracks tend to be something like "The game's changed while you were away, old man!" The next words, usually said a few minutes later, tend to be something like "Man! The Rocket's no joke!" while their mechs are either flat on the track or in some other pants-down situation. However, Andrei is a mild subversion. While his tactics still leave pilots reeling, his body can't keep up nearly as well as it used to: the years between his retirement and his temporary comeback were not kind to him.
Happosai and Cologne from Ranma ½ who are both 100+ years old and roughly one foot tall. While Cologne plays this trope straight, Happosai more or less inverts it. He barely has any interest in martial arts, and his efforts as a sensei means he can, charitably, be described as a Fair Weather Mentor. He's a major-league Panty Thief and Lovable Sex Maniac (only without the lovable), to the extent that he literally gets weak and sickly, losing the majority of his martial arts prowess, if prevented from stealing underwear and groping women. Yet, despite this almost completely opposed personality and the fact he considers being a pervert far more important and meaningful to being a martial artist he is still an incredibly powerful fighter, capable of smacking down PantyhoseTaro with one of his normally firecracker-grade bomb attacks.
Jiji from Ichi The Killer wears baggy clothing and walks with a slump in order to disguise his true strength.
Naruto has the Third Hokage, who despite being a decrepit-looking 70-year-old man, is extremely powerful and skilled, able to go toe-to-toe with the likes of the Big Bad Orochimaru. Many have called him one of the most powerful Shinobi to come out of the Leaf Village, perhaps equaling or even surpassing the late Fourth Hokage. A shame he dies, but even then he fights to the bitter end, sealing Orochimaru's arms and thus rendering them dead and useless.
In that vein we also have Jiraiya, who is the strongest of all three Sannin, could kill three paths of Pain (up until then, that was practically impossible), permanently kill one path, and was the master to Naruto himself. Not only that, there's his master, Fukasaku, an 800 year old toad and one of the most powerful beings in Naruto. He also fits the trope The Yoda.
I don't know. Jiraiya seems more like The Obi-Wan. The REAL Old Master is Fukasaku.
Prince Kamehame, despite being 70 years old and having a bum heel, is able to defeat Kinnikuman via pinfall in only seven seconds. In the Dream Choujin Tag Arc, he wrestles alongside Kinnikuman in his Kinnikuman Great guise, and they defeat Black Hole and Pentagon together before he's mortally injured by Sunshine's Cursed Roller.
Vagabond (the Takehiko Inoue manga) has four for Miyamoto Musashi: his father Shinmen Munisai, Houzouin In'ei, Yagyuu Sekishuusai are all Musashi's Old Masters (to a point), yet subvert the trope in their own ways: Munisai wasn't much of a master (his obsession with being "invincible under the sun" actually left him closing off his world, fearing his own child and pushing away others), In'ei was actually Inshun's Old Master and trained Musashi because no one else could threaten Inshun's life and thus get Inshun to develop further, and Sekishuusai is 'just' an old man who's since retired, passing down the system to his son; what he does impart onto Musashi is one of the most profound lessons, after Musashi defeats himself by internalizing the idea of "the invincible Sekishuusai" until it becomes a Self-Fulfilling Prophecy: "Invincible's just a word."
Sasaki Kojirou's adoptive father Kanemaki Jisai subverts the trope too: living by the sword has left him unmarried, without children or friends, and thus hopeless... until Kojirou comes along; at that point, he advertises himself (unsuccessfully) as an Old Master to make a living so that he could raise Kojirou away from the sword. When Kojirou shows a terrifying affinity for the sword (by disarming an evil Old Master and then attacking the corpse) however, Jisai spending the next half of the boy's life embodying the phrase "old age and trickery beat youth and speed," trying to repeatedly dissuade the boy by defeating his challenges with cunning and underhanded means... until his former disciple Itou Ittousai comes along and secretly takes Kojirou under his wing. After he finds out, Jisai reluctantly gives up Kojirou into Ittousai's custody, thinking that he gave his life to the sword only to have nothing but regrets... until he finds that although he couldn't keep Kojirou away from the sword, he did raise a decent man with great potential. "My life dedicated to the sword — it was worth it all. It was worth it because I managed to leave behind a great swordsman like you..."
Genkai from YuYu Hakusho, the defining example of the "just wants a break" version, and badass grandma.
Saiyuki: When Genjo Sanzo meets Master Abbot Jikaku in the Burial arc, he seems like just a harmless old man- until he kills several youkai attacking a temple. Turns out he was once known as 'The Ogre' for his vicious training of would-be Sanzo candidates, including Sanzo's own master Koumyou.
One Piece: Whitebeard, Sengoku, Rayleigh, and Garp among many others. It helps that if you're a pirate or a marine the only way you can live to see old age is by being stronger and more badass than everyone else.
Tenchi Muyo!: Katsuhito Masaki in the OAV series (actually he's quite formidable in all of his incarnations, but...). Granted, he's really a young man — relatively; where he's from, 725 years plus or minus is considered youthful — masquerading as an old man, but even the trope's description warns us that looks can be deceiving. Capable of taking on even the most powerful villains in the galaxy and fighting them to a draw, if not actually winning.
Tears To Tiara's Master Ogam. While he spends much of the early episodes as the calm and serious old guy, it's not long before he breaks out his MAGICAL POWERS and blows up an ogre.
Toriko: Knocking Master Jirou fits the bill, as demonstrated when he effortlessly paralyzed a beast that took the combined might of Toriko and Coco to bring down. Later on, the IGO president shows us that he also qualifies.
Baki the Grappler has several: Doppo Orochi, Gouki Shibukawa, Kaku Kaioh and Ryu Kaioh...and not one of them stands a chance against Yujiro.
Makarov Dreyar of Fairy Tail. 88 years old (actually 96, thanks to spending seven years frozen in time), incredibly powerful, and master of several different types of magic, on top of being one of the ten Wizard Saints. That title is only granted to the most powerful wizards in the land, and it's implied a few times that Makarov is one of - if not the - strongest of all of them.
Hayato Furinji of History's Strongest Disciple Kenichi. He is the undisputed most experienced and powerful master in a series filled to the brim with martial arts masters. Unlike many other Old Masters, though, Hayato still has an imposing physique: the man is huge and extremely buff despite his advanced age.
In School Rumble, Mikoto finds Hinai training in the mountains, with an old man dispensing mystical-sounding advice. Mikoto Hinai if he's his sensei, but Hinai responds that it's just some random old guy.
And of course, one cannot forget the unnamed Master in The Frantics' legendary "Tae Kwon Leep" skit.
Archie Comics: He's not that old, but the students of Riverdale High underestimated Coach Kleats in several sports. The same thing happened, with the entire male faculty challenging the varsity basketball players to a charity game.
Ekuar in ElfQuest, tutor of Rayek, definitely qualifies. Despite having endured centuries of imprisonment, mutilation and torture at the hands of the trolls, he never lost his wisdom or his wicked sense of humor.
Katsuichi-sensei, the hermit who taught Usagi just about everything he knows, is at least a Middle-aged Master.
In the first few issues of Ninja High School, Ichiban fights her grandfather... Well, she challenges him anyway. Fight ends before it begins.
Stick from Dare Devil. Even being dead doesn't stop him from coming back every couple of years, to dispense some sage advice.
Dr. Yagyu from Nth Man: The Ultimate Ninja is a Ninja master in his late 60s, but thinks nothing of stepping into a war zone with a satchel full of throwing stars and a machine pistol.
The Ancient One, mentor to Doctor Strange. He managed to stretch his lifespan to about 600 years and was still in reasonably good physical and mental health when he died.
Film - Animated
Played a bit in Kung Fu Panda where Shifu is the old master to the Furious Five and Po, but he himself has more to learn from both his own mentor, Master Oogway, and from Po's own insight.
Played completely straight with extremely pacifist and soft-spoken Oogway himself (Who is about 1000 years old), to the point that he was originally able to take down the undefeatable Big Bad in less than a second.
Rafiki from The Lion King ends the film kicking some serious hyena butt.
Film - Live Action
The most famous example is, without a doubt, Mr. Miyagi from The Karate Kid.
Grand Master Yoda, in the Star Wars films, especially his first appearance in The Empire Strikes Back. Thanks to CGI, fans got to see him in action in Attack of the Clones and Revenge of the Sith, as well as the "micro-series" Clone Wars.
Also Count Dooku in Episode II, who, while established as a ex-Jedi early in the film, is only revealed as a master swordsman when he neatly trounces Obi-Wan and Anakin during the final battle — until the arrival of the other Old Master, of course.
Obi-Wan in Episode IV, Sidious in III, and the Emperor in VI, are all introduced as physically frail old men who unleash previously unseen powers or abilities by the end of the film. Obi-Wan literally "become[s] more powerful than you can possibly imagine".
Pai Mei in Kill Bill: Volume 2. He's more of a cruel and evil master than the kindly Mr. Miyagi type and according to the film's mythology was responsible for the destruction of the Shaolin Temple because a Shaolin monk that he passed on the road didn't return the slight nod that he gave him. He's been known to snatch out the eyes of those who look on him with defiance and snap the backs and necks of those who give him sass like they were twigs. This eventually gets him killed when he snatches out Elle Driver's right eye for calling him a "miserable old fool," and she retaliates by poisoning his fish heads. He hates Caucasians, despises Americans and has nothing but contempt for women. So of course his greatest student, the only one he teaches his Five Point Palm Exploding Heart Technique, is a blonde Americanwoman. Who also leans to love him as a father, joyfully snatching out Driver's left eye as vengeance for him.
Remo Williams: The Adventure Begins subverts this by making its old Korean mentor capable of assorted miraculous feats but also a blatant racist and sexist. He is from a different generation.
Incidentally, the old Korean mentor's racism consists entirely of Korean chauvinism, which makes him a neat parody of the kinds of racists Western audiences are more likely to encounter.
The pretty badCrossworlds stars Rutger Hauer as one of these.
The gatekeeper in Stardust. ("The man must be 90 years old." "Well, then, he's had plenty of time to practice, hasn't he?"
Red appears to be this, with a team of retired black-ops investigating their former employer.
Practically the archetypal example, and the one that Lu Tze's quote was, in its original context, a Shout Out to, is the kung fu movie sifu. Practically every one of Jackie Chan's '70s to '80s kung-fu movies (not to mention the similar movies starring other actors) featured an Old Master who looked like a strong gust of wind should knock him over but who invariably mopped the floor with not only rooms full of mooks but also Jackie Chan himself until he learned to respect his elders. Most famously the film Drunken Master, but many others. Arguably inspired both Obi Wan Kenobi and Yoda in the Star Wars milieu; almost certainly inspired Mr. Miyagi.
Deconstructed in Ip Man 2. While Master Hung is kickass enough to hold his own against Ip and the Twister at first, the length of the exhibition match causes exhaustion to start setting in leading to his death.
Eda Bell, one of the two teachers of hand-to-hand combat in Tamora Pierce's Kel books says something to the effect of 'I may look like someone's grandmother, but some grandchildren require more raising than others.'
In the Lost Fleet series of books by Jack Campbell, Captain John Geary has spent a century in Suspended Animation while his reputation became Shrouded in Myth... and everyone else forgot effective naval tactics in favor of simply charging at the enemy. Which means once he takes command, forces that follow his orders tend to win amazingly one-sided victories unless ridiculously outnumbered — then they just win.
Mazer Rackham in Ender's Game, hero of the second Bug War and Ender's trainer in the third one.
Kaa in The Jungle Book. The oldest creature in the jungle, Kaa offers sage advice to those who seek it, and painful, suffocating death to those who cross him. Or happen to be near him when he is hungry. He doesn't discriminate that much.
Ser Barristan Selmy from A Song of Ice and Fire. He's the last living member of King Aerys' old Kingsguard, if you leave Jaime Lannister out of the count, and can easily defeat younger adversaries.
Also from this book, Syrio Forel, the first sword of Braavos, who takes on several Mooks to protect Arya while she escapes, and bludgeons them to death with a wooden sword. He dies a few minutes later to a knight, though. In his defense, the knight was wearing armor and he was aware that the fight was hopeless.
Harry Potter: Dumbledore is clearly a prime example. He's incredibly old, but most people speak of him in complete awe. In the fifth book we probably get the best view of his power when he takes down three ministry officials (with a little help) and then battles Voldemort to a draw after restraining some half a dozen Death Eaters. This is likely due to the fact that in the wizarding world knowledge actually equals power and Dumbledore has had plenty of training time.
Some of the other teachers at Hogwarts qualify. Flitwick, it's mentioned somewhere, is an old duelling champion. McGonagall is powerful enough to enchant the school itself to come to life and use it as a weapon. She, Slughorn and Sprout duel Voldemort in the final book. Naturally, they are also masters in their respective fields - or they wouldn't be teachers.
Another example is (probably) Augusta Longbottom. We never actually hear what she's a master of, but she's incredibly powerful.
In Emergence, by David R. Palmer, the character referred to by the narrator as "Teacher" or "Master" (depending on context. Name is given as Soo Kim McDivott) plays this role for the narrator and several other characters.
The Discworld has Cohen the Barbarian, the greatest (and oldest) barbarian hero in the world. Those who underestimate him because of his age don't realize that living to be over seventy in a dangerous profession such as barbarian heroism means he's good at it. The book Interesting Times introduced the Silver Horde, a group consisting of Cohen and some of his fellow elderly barbarians, all of whom are still incredibly dangerous (despite one of them being in a wheelchair). The seven of them conquered a continent roughly analogous to China.
Six Beneficient Winds: But ... they're so old!
Mr Saveloy: Indeed, and of course, this is true. They are very old barbarian heroes.
Six Beneficient Winds: Oh, my ...
Mr Saveloy: That's right. They've had a lifetime's experience of not dying. They've become very good at it." ...
... And Mr Saveloy could see it dawning in the fat man's eyes.
There is also the previously mentioned Lu-Tze, who first appeared in Small Gods, but really got to strut his stuff in Thief of Time. And Lu-Tze mastered the technique (mentioned with Cohen earlier) of letting his reputation precede him: particularly Rule #1.
Rule #1: Do not act incautiously when confronting little bald wrinkly smiling men.
Because, although he rarely uses it, Lu-Tze has the capability to knock even the personification of Time for a loop.
On another branch is Granny Weatherwax. What she lacks in physical skills, she more than makes up for in her knowledge of Discworld psychology (or "headology", as she puts it). She is no less a master of reputation than Cohen or Lu-Tze, and reputation and psychology are her primary weapons. Like Lu-Tze, everyone questions whether she is a real witch, but she has shown the ability (if not the eagerness) to perform very powerful magic when she really needs it.
Such as when she moved the entire kingdom of Lancre forward in time 15 years (in Wyrd Sisters).
Druss from David Gemmell's first published novel, Legend, is an unusually blunt variant of this trope. Sixty years old, built like a bull, and quite capable of single-handedly slaughtering a dozen men half his age. His presence, and wisdom, inspire the younger characters to heroism; after all, he is a living legend. Meanwhile, he's trying to pretend he's not half-dead from exhaustion, agonised by arthritis, and determined to avoid senility through battle.
Larkin and Mkoll from Warhammer 40000: Gaunt's Ghosts, respectively (almost) the best sniper and the best scout of their regiment. Admittedly not that old.
Mkoll was canonically the father of adult children (and probably grandchildren) before the series started, but they all died in the annihilation of Tanith. Similarly, Doc Dorden had a grown son in the regiment at the start of the series. A lot of the Tanith are quite old for Guardsmen. But then, you only have to survive one battle to be quite old for a Guardsman...
Eldrad Ulthran, the late leader of Ulthwe craftworld. More than 10,000 years old, so old that his body has begun to crystallise. Before he was lost to a talisman of vaul, he was arguably the galaxy's most powerful living psyker. In fact, he was able to defeat Abaddon, one of the greatest warriors aligned with Chaos, in hand-to-hand combat by using his prescience to stall until the single perfect moment to strike.
Colbey Calistinsson, from The Last Of The Renshai trilogy. Never mind that he is 67, in an era where people seldom lived to 40. He was perfectly calm about taking out a group of 15, training a 16 year old girl in the art of the sword, fighting a group of 100 with only Santagithi to help him, and an army of 10000 quaracks, by himself
Santagithi is also a very competent swordsman, at the age of 58, waiting until the end of the battle to die, because he tripped on a rock
The Renshai race, which Colbey was a part of, almost never lived to the age of 25
Belgarath, sure he looks like a scruffy old vagabond, but he's also 7000 years old and the single most powerful sorcerer EVER. The Big Bad's followers consider him to be Satan and need a change of underwear at the mention of his name.
In The Destroyer series of novels, 80 year old (at least) tiny Chiun is quite literally, the most dangerous man in the world. If he wants you dead, you might as well shoot yourself.
Conan the Barbarian by Robert E. Howard: In "The Tower of Elephant" Conan meets Taurus, whom he has heard of as "the prince of thieves." Taurus, liking his spirit, takes him along and immediately instructs him.
"You made one mistake," said Conan. Taurus' eyes flashed angrily. "I? I, a mistake? Impossible!" "You should have dragged the body into the bushes." "Said the novice to the master of the art. They will not change the guard until past midnight. Should any come searching for him now, and find his body, they would flee at once to Yara, bellowing the news, and give us time to escape. Were they not to find it, they'd go beating up the bushes and catch us like rats in a trap."
Subverted in The Wise Man's Fear where Shehyn, the elderly teacher of an order of legendary fighters, battles one of her much younger students, the student much more energetic vs Shehyn's measured movements - and Shehyn loses. Kvothe wonders if this means the one who beat her is the leader now, which the member he's talking to finds amusing. Not only would it be ridiculous to base their leadership off of who wins a single fight, but Shehyn is very old. It's not realistic to expect her to always beat someone with much more energy. Of course, Shehyn is still extremely good.
Bodger from The Incredible Journey is a goofy, half-blind old bull terrier whose goal in life seems to be to mooch as much love and food from humans as possible. He is also a dog fighting veteran and can still beat up other dogs when he needs to.
Live Action TV
In the 2003 version of Battlestar Galactica, the main character, Commander Bill Adama is an Old Master. His morals and ethics dictate the conduct of the rest of the crew (i.e. characters remarking on more than one occasion "Cmdr. Adama would/would not do this"), and he openly regards many of them like children to him (which is extremely worrisome when you consider his terrible relationship with Lee, his actual son). This does not change the fact that, as we see in the season one episode "Kobol's Last Gleaming, Part 1", and the season three episode "Unfinished Business", Bill's capable of stepping into the boxing ring the crew has set up and beating the stuffing out of said "children" should he feel the need.
He's pretty handy with a flashlight, too.
Grasshopper, Master Po from Kung Fu, surely one of the Trope Makers of the Old Master, and owner/operator of a Disability Superpower to boot. Or The Ancient One from Kung Fu The Legend Continues, who might have been several hundred years old.
Master BratakBra'tac of Stargate SG-1. In his first appearance in the series, started off by complaining about his old age, then promptly incapacitated Colonel O'Neill in an embarassingly short fight sequence. Continues to refer to himself as an old man during the entire 10 seasons despite the fact that he is obviously one of the most skilled warriors in the galaxy.
Due to his 50 years spent in a time warp in SG-1's final episode, Teal'c is even older than Bra'tac now. As of that episode, he's nearly 160 in subjective years. That makes him physically about 5 years Bra'tac's senior!
Though he doesn't look it. Turns out, the time warp being 50 years was the result of a makeup error that couldn't be corrected before the deadline. The writers originally intended it to be "merely" around 20 years, so that Teal'c would still be a quarter century younger than Bra'tac.
In "Worst Nightmare", the NCIS team has a difficult time keeping up with the grandfather of a missing girl.
What do you mean "in 'Worst Nightmare'"? Gibbs himself should be the first example, and his former boss and teacher Mike Franks should easily qualify.
Both played straight and averted in Power Rangers Jungle Fury; some of the masters and teachers from the Order of the Claw are indeed old masters. However, in the first episode, when the rangers are sent to the Jungle Karma Pizza restaurant to find their new master, they see a man who looks like your stereotypical old master and immidiately assume he must be the one they are searching for, only to find out he is just a customer and the real master is the much younger owner of the restaurant.
A non-combat example from Star Trek: The Next Generation is seen in Unification, when Spock instantly and accurately figures out the details and major players of a Romulan plot before Picard—or even Data, who is arguably more intelligent than Spock—even have a chance to draw a breath.
Star Trek: Deep Space Nine shows the later years of Dahar Master Kor, who despite suffering dementia, is able to hold off a fleet of Jem'Hadar fighters with a skeleton crew on a crippled bird-of-prey long enough for Martok's task force to get away.
Fellow Dahar Masters Kang and Koloth—with the help of Jadzia Dax—defeat the albino's army with little effort in Blood Oath.
The Old Master archetype from Feng Shui has the highest starting Martial Arts and Chi scores of the whole archetype list and five Fu Schticks, and though he only starts with a Body score of 4, his Unique Schtick allows him to use unarmed attacks to wallop characters with 10 base damage (equivalent of Body 8 or 9). You just know it's a bad move to mess with him.
Monks in Dungeons & Dragons eventually gain Timeless Body, which means that while they still visibly age they take no penalties for aging and are every bit as physically powerful as they were at their prime. At the level a monk gains that ability he/she is also not to be trifled with, or at least not unless you're pretty much any other class at the same level.
Sebastian Crenshaw from Mutant Chronicles. Picture Ryu Hayabusa as played by Sean Connery. 55 years old in a universe where average life expectancy is 40, but still the Solar system's most skilled assassin, swordsman and martial artist.
Warhammer 40K has Chapter Masters of the Space Marines who only get there by earning the respect of an entire chapter. Usually done by at the very least, surviving and distinguishing yourself in centuries of battle against nightmarish odds in a crapsack universe.
In Assassins Creed, the single most dangerous opponent you can face in a straight sword fight? Your own ancient, gray-bearded master, Al-Mualim, in the final battle.
Though he isn't any better with his sword than other major opponents; instead he uses extensive trickery. Being able to magically multiply yourself has some clear advantages in battle.
Plus, he can be insta-killed with the Hidden Blade, just like every other NPC.
Although his true age is unknown, La Volpe from the sequel is clearly no spring chicken as his wrinkled face shows. Nevertheless, the first time Ezio meets him, the former is winded trying to keep him.
Final Fantasy XI has Maat, the old man responsible for raising the level cap from 50 to 75 (or just to 70 on a few expansion jobs). He uses both Wax On, Wax Off and Training from Hell methods to raise your limits, but you never take him too seriously, and think he's just an advisor... then you go to break the 70-75 cap, which has you fight him, and most likely see him gleefully rend you into paste, even unfairly so. Simply put, anyone who's 75 respects him. Or hates him. It kinda varies.
Love him or hate him, you have to respect him. Even if you fought Maat as a Red Mage back in the days before he was nerfed, you have to smile when you see Maat whalloping the crap out of enemies in the past in the Wings of the Goddess expansion.
By extension Emperor Sun Li, who is Master Li's elder brother.
JoleeBindo in Knights of the Old Republic, who is old enough to be starting to lose his memory and for the little hair he has left to be completely bald, and yet with the proper build and gear is a contender for the title of most powerful character (including the player) in the game at high levels.
Saisyu Kusanagi, Chin Gensai, Takuma Sakazaki, and a number of others from The King of Fighters. Several of them got together to form the Old Man Team one year: Saisyu, Takuma and Colonel Badass Heidern (despite them not being that old, compared to Chin). In KOF 2002 Unlimited Match, Chin joins the team in Saisyu's place, due to the game being a dream match for the 99 to 2002 editions and Bao occupying his position in the Psycho Soldier team.
Also Tung Fu-Rue and Jubei Yamada from the Fatal Fury series, along with Lee Pai-Long from Art Of Fighting. Tung even made it as a bonus character in the PS2 version of KOF XI. Makes you wonder why they didn't form a Badass Grandpa team in KOF.
In Ōkami, the sensei which teaches you new moves starts out when he first talks to you as a kind old man....but when you purchase a new move his head literally spins completely around, turning his giant chin into a giant forehead, and his long mustache into badass eyebrows, and his back straightens out, and his cane becomes a bamboo riding crop.
The Master from Paper Mario. While he appears to be asthmatic and weak, when he goes quite literally Super Saiyan on Mario, he turns out to be quite possibly the game's hardest foe.
In the Mortal Kombat series, Bo Rai Cho fills this roll. An ancient martial artist native to the Outworld who invented Drunken Fist, his many students include Li Mei, Kung Lao, and Liu Kang, the hero of the series. And he's no slouch himself. (In Mortal Kombat Deadly Alliance, it is stated that the only reason he never took part in the original tournament in an attempt to defeat Shung Ti himself is because, as an Outworld native, Shao Khan would get credit for his victory, which was what Khan wanted in the first place.)
Played straight in Phantasy Star Universe with Headmaster Nav - the only difference being that he's a CAST (an android) who only looks like an old man. He's still almost 200 years old, though.
Ford Cruller, from Psychonauts, is a skilled and powerful Psychonaut, but after a fierce psychic battle long ago, he suffered brain damage that causes him to develop a Split Personality when he gets too far from a source of Psitanium (like that beneath Whispering Rocks camp). So instead, he works as Mission Control when he's not doing odd jobs around Whispering Rocks. He also ends up becoming Raz's psychic tutor.
Sotaro Komaki from Ryu Ga Gotoku embodies this trope in the game.
Gen from the Street Fighter games. He's actually a Blood Knight in at least his 70's who is deathly ill but prefers to die in a fight than succumb to his illness.
Also from Street Fighter, Gouken, the elder brother of Akuma and the legendary master of Ryu and Ken. Initially only known through backstory and rumors, he was finally made playable in the home ports of Street Fighter IV.
Oro from III, an elderly hermit who is 140-years-young and still more powerful than the average young fighter in their prime. So much that he voluntarily disables one of his arms just to even the odds for his opponent.
In Super Punch-Out on the SNES, you fight a Chinese martial arts master called Hoy Quarlow. He is both the most unorthodox and most irritating opponent in the game, not so much for his difficulty (he is indeed a tough opponent), but for the fact he unabashedly cheats; half the time he doesn't punch you, but kicks you and hits you with his walking stick. In a boxing game. You can guess that he's That One Boss...
Master Rishu from Super Robot WarsOriginal Generation deserves a mention here. While being a side character who is only mentioned to be Sanger's teacher in the first game, and using a cane to walk, he was more than capable to take on multiple bioroids armed with automatic weapons while using only a sword, hidden in his cane. Later, in OG 2.5 he becomes an actual playable character, piloting Grungust type 0.
Wang Jinrei from the Tekken series. When he participates in The King of Iron Fist Tournament 5, he's 105 years old, has a bad back, and is somewhat senile. He can still send the young'uns tumbling across the arena with ease, however...
Master Zen, the ancient martial arts master in Tony Hawk's American Wasteland. For some reason, his teaching translate very well to skateboarding while still conveying supernatural abilities. He's also a total goofball, in spite of his wisdom.
All four of the Dragon Guardians from The Legend of Spyro trilogy. While their age isn't mentioned, their words imply they're getting too old for the job, but that doesn't mean the Apes attacking the temple in the second game didn't get their butts kicked by the four of them. Yeah, Spyro and Cynder outclass them in the end, but that's what they were hoping for.
Edge Master from the Soul Series. He is Kilik's master and can also use every weapon in the game with equal proficiency to its owner. One of the oldest, non-immortal characters in the series (though his actual age is unknown).
The Greybeards from The Elder Scrolls V Skyrim. They have trained their voices to such an incredible extent that even a misplaced whisper could kill you instantly. When they greet you with a politely whispered "Dovahkiin", the whole mountain shakes from the force of it. When they spoke in full voice to summon you to High Hrothgar, all of Skyrim heard it.
In Pokemon Red And Blue, there was originally going to be a battle with Prof. Oak, who apparently keeps the Pokémon neither you nor your rival chooses. He would have been the strongest Trainer in the game - even better than the Champion - but, for some reason, the battle was dummied out. However, using a Game Shark, the battle can still be accessed.
Augus from Asura's Wrath, a Cool Old Guy who is quite fond of the finer things in life and has quite the Blood Knight streak to him. Unfortunately, he's also one of the Seven Deities who Asura has sworn vengeance against for betraying him. The battle you have against him is one of the most awesome ones of the game.
The Old Man and Prof. Oak from Pokémon, according to this video.
Sensei Ito of the Whateley Universe. He is a little old man without powers who teaches martial arts to teens who are mutants with superpowers. In his first appearance (the first day of classes), he schools PK superboy Lancer. In later stories, we learn that Lancer was the fourth superpowered teen he clobbered that day.
Bruce Wayne from Batman Beyond is definitely an example of this trope. Stooped over and forced to rely on a cane to help him walk, he still stares daggers through anyone who would presume to show him his place, and is more than capable of beating the holy howling tar out of an entire motorcycle gang by himself, standing almost completely still, with nothing but his cane. This plus his still-razor-sharp mind and the experience of his years as the original Batman makes him somehow more intimidating than when he was in his physical prime. This was proven in an episode where his younger self visited the future, forcing Batman to play good cop to Old Man Wayne.
Old Man Wayne: I can't believe I was ever that green. (He grabs the thug away from Batman.) This is how you interrogate someone!
Cut to the gang member telling the Old Man everything up to and including that he wet the bed until he was a teenager.
Another example in the DC Animated Universe, much earlier on, is Batman's own master; Yoru Sensei, who quickly immobilizes Kyodai Ken, just shortly after Kyodai beat Bruce Wayne in a sparring match. Given that Kyodai was less than half Yoru Sensei's age, and Yoru Sensei himself looks very much like the man in the example picture, he definitely qualifies.
In Teen Titans there was the True Master (named Chu Hui in the end credits) a rare female example of this trope. Her habit of giving answers that had simple meanings when people expected complicated ones was very similar to Mr. Miyagi's habit of doing so.
Avatar The Last Airbender: King Bumi, Uncle Iroh, Jeong Jeong, Master Pakku and Monk Gyatso are all prime examples of this trope, each being one of the most powerful of their respective elemental bending discipline (Iroh and Bumi make heavy use of Obfuscating Stupidity as well). Although never seen in combat, Monk Gyatso qualifies because of the amount of dead Firebenders surrounding his corpse he fought during Sozin's comet, . Whether or not Piandao counts is based solely on how old you think he is. In the Grand Finale, King Bumi, Uncle Iroh, Jeong Jeong, Master Pakku and Piandao all show up and take back Ba Sing Se themselves. For bonus points, the episode in which we see them is actually named "The Old Masters"
Spoofed in the George of the Jungle episode "Still Got It", in the form of Grouch-Mouth. He's an elderly tiger who gets picked on at first but," You're forgeting that Ol' Grouch-Mouth is the king of the pranks." He then gets in his scooter and goes on a pranking rampage, until the now-decrepit "Mighty Berment" (who originally defeated him) arrives. The two fight. While the fight was anticlimactic, it turns out the two are old friends and join forces to show how pranks are really done. They go on an even bigger pranking rampage, which was a Crowning Moment of Funny. George ends up sending Berments Wife, Mighty Mary, to save the day and the two pranksters leave.
Uncle in Jackie Chan Adventures. Not only is he an expert Martial Artist, but also one of the most powerful Chi Wizards in the world, helping his nephew save the world on a regular basis with his extensive magic.
Master Panda of Skunk Fu! is a textbook example of this.
In one Stargate Infinity episode, the crew met a race of squirrel people. To cross a bridge a kindly old man requests that one of the team fight him. When the Action Girl tries and gets her ass handed to her, the team leader quips:
"When an old man challenges you to a fight, you've got to figure he's either crazy, or knows something you don't. This guy didn't look that crazy to me."
Scavenger in Transformers Armada. Not only is he the kind of fighter badass enough to catch a blow from an unstoppably powerful sword with his arm, but he makes a pretty good double agent.
Master Fung of Xiaolin Showdown is a classic example, being an actual Chinese monk. Not only is he filled with wisdom (And the cheesy sayings that come with it), he's also a force to be reckoned with when he fights, taking on several of Chase Young's tiger minions at once and winning, and in one instance, fighting Chase and Wuya in a wheelchair and holding his own. However, due to his age, he doesn't quite have the energy to keep it up...
In Japan he is referred to as O-Sensei, the Great Teacher. He's the Old Master of other Old Masters. It helps that Aikido is based on passivity and indirectness, but seriously, that guy was like 90 pounds.
According to Shiji, the King of Wu was so impressed by Sun Tzu that he appointed him General after his first audience. Sun Tzu went on to enable several crushing military victories and establish the State of Wu as the dominant power in the region.
Almost every old martial arts master who has kept in practice with his/her martial art of choice seems to be as strong as and even quicker than their fittest young students.
They don't need to be quicker. They have seen all the tricks anyone could possibly attempt before.
They also have refined their sense of timing to the point that regardless of how fast you are, they are still where they need to be before you are.
This trope is actually enforced by several martial arts; once you hit black belt, you can only go up in rank provided you are old enough. For example, in Kobudo, to get to 10th Dan, you have to be 72 years old, minimum.
They also don't need to be stronger. They can use angles to their advantage.
One of the most important things to learn in fighting is how to control the fight. Experience teaches you your strengths, weaknesses, and how to use those to make your opponent fight to your benefit.
The late, the great, Helio Gracie, one of the founders of Brazilian Jiujitsu. He continued to train hard and utilise the martial art he helped to create until his death at the age of 95.
A 24-year-old mugger with a knife made the mistake of breaking into 72-year-old Frank Corti's home and threatened him and his wife. Corti, a former boxer, beat the mugger's left eye and mouth purple with two punches.
A newspaper story concerned three youths who mugged a retired gentleman in his sixties as he left a London Underground station late at night. Unfortunately for them, the job he had recently retired from was thirty years teaching unarmed combat to the SAS. His attackers were arrested in hospital.
Master Lau Kar Leung. A veteranactionstar of the Hong Kong Cinema (he is best known for his movies which he made during the 1970s and 1980s for the Shaw Brothers Studio) as well as director and fight choreographer, as well as the grand master and practitioner of Hung Gar style of Kung Fu system (the inspiration for earthbending), which was made famous by Chinese hero Wong Fei-Hung. Yes, that Wong Fei-Hung. Interestingly, Sifu Lau's father, Lau Cham, was a student of Lam Sai Wing, pupil of the legendary Wong Fei Hung. Today, he's in his late 70's and is still very much active in films choreographing fight scenes, and he is well respected from his colleagues and peers. His last starring role (as of yet) is in the film Drunken Monkey, and as you can see, he's not mellowing with age. (He's almost 70 years old there, for crying out loud!)
Anko Itosu, one of the founders of modern Karate, took on a much-publicized challenge for a fight between Judo (the Japanese Martial-Art) and Karate (the Okinawan Style) when he was in his late seventies. The Japanese were insulted and the Judo champion spent the first few minutes of the fight mocking the old man. Itosu threwonepunch, the other guy hit the ground, and then Itosu helped revive the unconscious Judo champion.
Lu Zijian, reportedly 117 or 118 years old, said to have lived in three centuries, and master of huolong taiyi tai chi. The man has aged amazingly well and was known to have mopped the floor with opponents in his youth. The man actively started joined all the martial arts contests he could find...at the ripe old age of 86.
Not quite as old as most of these examples, but Bernard Hopkins continues to dominate in boxing at 46. Remember one thing, most boxers are considered old and faded by the time they get into their mid-thirties, so in boxing years, Hopkins (or rather Master Hopkins, as most boxing fans are beginning to refer to him now) is absolutely ancient and is still handling guys half his age. In fact, in June 2011, Hopkins became the oldest boxer ever to win a major world championship when he defeated Jean Pascal to win the WBC, IBO and The Ring Light Heavyweight belts.
In the world of film soundtracks and Orchestral Bombing, when all modern scores are dominated by computer and electronic software, John Williams showed why he is still intellectually superior with the 2012 releases of War Horse and The Adventures of Tintin. This composer (yes, the same one that also gave you the unforgettable scores from Superman, StarWars and the Indiana Jones films of 30 years ago) is over 80 years old. How did he celebrate his 70th birthday? By conducting the Salt Lake City symphony orchestra performing the theme song he composed for the XIX Winter Olympic Games, at the Opening Ceremony.
Frank Lee. One of the pioneers of martial arts in Western Canada by introducing White Crane Kung Fu and Muy Thai there. Black Belt magazine once called him the Father of Kickboxing in North America. He's in his 70s and still teaching his own brand of mixed martial arts, which he evolved when he was in a number of street fights and bar brawls as an immigrant. A couple of tough fights and he realized his kung-fu wasn't well-rounded enough to last against experienced fighters who've had a chance to wise up, so he started adding elements from other fighting arts including boxing and Greco-Roman wrestling.