Joey/Jonouchi defeats an opponent by allowing his Baby Dragon to age a millennium into the much-more-powerful Thousand Dragon.
It's also true with Yugi's Dark/Black Magician, who becomes the Dark/Black Robed Sage after also having a thousand years to study the arts of magic.
The Gagagigo story shows that Gagagigo became stronger when he ages. However, while Gagagigo is much stronger than his child self "Gigobyte", his cyborg version "Giga Gagagigo" was modified by Kozaky, averting this trope. "Gogiga Gagagigo" was the stronger, insane version of "Giga Gagagigo", but he eventually became the good "Gagagigo the Risen" who has the same ATK and DEF as "Gogiga Gagagigo".
The Lyrical Nanoha franchise has Voltaire, an ancient black dragon so powerful, it's practically revered as a Physical God in Caro's home planet of Alzus, with Caro serving as a priestess that it occassionally lends its power to. In contrast, Friedrich, the young dragon that Caro raised on her own, is mainly used for support fire and transport even in his full form.
The Saiyans in Dragon Ball, with the added bonus of a leap in power whenever they recover from near-fatal injury. In Dragon Ball Kai, Doctor Gero says this shouldn't happen, and that any powerup Goku got after the Saiyan saga would be more or less negated by his age. He's immediately proven wrong when Goku goes Super Saiyan. Age is never shown to slow down Goku or Vegeta.
Frieza's father, King Kold, also deserves a mention, since most fans speculate that he had to be even stronger than Frieza was, in order to control him.
In Kingdom Come Superman is said to be undergoing this. After so many years under Earth's yellow sun, he's stronger than ever, and immune to Kryptonite.
Grant Morrison's Superman gets more powerful over the next 80 millenia and eventually bestows powers on his descendants.
The Maestro, the future version of the Incredible Hulk, who is stronger and smarter than present day Hulk (even when PDH is in smart mode).
Part of the rationale is that there had been a nuclear war, and since the Hulk is radiation-powered, this made him stronger at the expense of his sanity (well, at the expense of Smart Hulk's sanity).
Anacondas: Hunt for the Blood Orchid uses this to justify Attack of the 50-Foot Whatever: the titular snakes are stated to keep growing for their entire life, thus ones that consume blood orchids—flowers that can prevent aging—can grow to be much bigger than normal.
The vampire Elders in Underworld are stronger than any other vampire and, in some cases, can even defeat lycans in hand-to-hand combat. In a memorable example, Viktor grabs Raze in his lycan form by the throat, holds him up for a few seconds, and then breaks his neck. In the case of Marcus and William, the Corvinus twins and progenitors of the vampires and lycans, respectively, they are also stronger, although this can be attributed to Monster Progenitor. In Marcus's case, his strength is augmented tenfold after he accidentally ingests lycan blood and becomes a hybrid. William was already stronger than any other lycan. According to Selene in Underworld: Evolution, Alexander Corvinus, the original immortal and the father of the twins, is easily the strongest of them all, although he refuses to fight or otherwise make use of it.
This is especially evident with Junior, who starts out like this◊ and grows up into this.◊
Mothra Leo in the spin-off Mothra Trilogy falls under this big time. In the third film, he travels back in time to the Mesezoic Era where ancient Mothra Larvae encase him in a cocoon for 65 million years before he emerges as Light-Speed Mothra before transforming into Armor Mothra and killing the evil Grand-King Ghidorah. And then he transforms into the immortal Eternal Mothra his most powerful form.
Elves. The more they age, the wiser and more powerful they are. However, it's implied that they become more 'hollowed out' by their own inner fires, and that after 1000 millennia (1,000,000 years) they may be spread thin.
The undead grow stronger the older the remains that went into their reanimation are. This culminates with Harry reanimating a Tyrannosaurus' skeleton. A Curb-Stomp Battle ensued.
Black Court Vampires. On the one hand, it is noted that since Mavra is such an old vampire she is likely to be mobile and capable of defending herself during the day where younger vamps would be forced to sleep. But then they toy with it by pointing out that the reason Black Court vamps in general are such major Badass types is because of basic survival of the fittest since Dracula was published. To get to be that old, they must have been Badass to begin with, or they'd have been killed (again) years ago.
Wizards also follow this rule - while part of it is that they learn how to more effectively use their power, even an increase of skill can't account for ALL of the tricks that more powerful wizards can pull off. Even WITHOUT the various external power boosts he gets, Harry has gained a noticeably greater degree of power over just the decade that the stories take place over; and significantly older wizards on the Council are capable of tricks Harry didn't even know were possible like dropping satellites from space with pinpoint accuracy and turning into a half-dozen animals in a bout with an Eldritch Abomination. This is aided by a wizard's slow aging and ability to eventually regenerate from even serious maiming without a build-up of scar tissue.
Also, Wizards minds are subject to this. The older they get, the more resistant their mind is to any type of mind control or persuasion. This little fact is used to great effect in one of the novels.
The vampires in Anne Rice's The Vampire Chronicles books get stronger as they age. Even after doing nothing but sleeping for hundreds of years, they wake up stronger than they were before. Drinking the blood of an older, more powerful vampire can also add to their power. They also obtain new abilities with age, or "gifts" as they call them, the most common one being the Cloud Gift which enables flight. Interestingly, no vampire is ever comfortable with flying, realizing how unnatural it is (even for a vampire), except for Akasha and Lestat (who gained these abilities after drinking her blood).
Eventually subverted in Mikhail Akhmanov's Arrivals from the Dark series, where the Dromi continue growing as they age, which initially does make them stronger with age. However, as they reach about 500-600 years old, the Square/Cube Law takes into effect, making it very difficult to move, and they eventually get crushed by their own weight.
The vampires in Barbara Hambly's Those Who Hunt the Night and sequels grow tougher as they age, eventually becoming resistant to their weaknesses - an ancient vampire such as Brother Anthony the Minorite can withstand the touch of silver that would burn and sicken a fledgling (newly created vampire) with even the slightest contact and even resist the light of the sun and the irresistible sleep that forces all younger vampires into a coma during the daytime hours. Their psychic powers (and presumably physical strength) also increase with age, although there are also possible, though inconsistent, degradations with age (the Bey of Constantinople, for example, can no longer create fledglings on his own).
In the Wiz Biz series by Rick Cook, dragons grow larger and more powerful with age, and have no known natural upper limit to their lifespans.
The Nobility in the Vampire Hunter D universe are also like this; and since the series takes place in the far future circa 12000 AD, where most of the time between now and then was dominated by vampiric rule following a nuclear Armageddon Twenty Minutes into the Future, some are very old indeed. Somewhat subverted in that a recent human uprising wiped out most vampires, and that those remaining, for all their terrible power, are a dying race. One of the recurring themes of the novel is that while humans are, on the whole, weak, short-lived, and otherwise flawed, vampires have an even greater, fundamental flaw which dooms them to eventual extinction; as the Revered Ancestor once put it when speaking about his kind, "Transient guests are we." It just so happens that D himself is the most successful result of a cross-breeding program by his father (the aforementioned Revered Ancestor) aimed at creating a new breed of vampires without this flaw, thereby ensuring the species' continuance.
Trolls in Discworld are theoretically immortal, but as they get older they get bigger and slower and tend to be more inclined to sit and think. They call this "getting philosophy". Eventually they just stop moving altogether, gradually "decomposing" or eroding into an oddly shaped heap of minerals with a tiny living spark in the center. Many of the Discworld's mountains are actually very old trolls. Shown to be true when a troll warns a character about his grandfather, who is one of the mountains and is very annoyed when some adventurers light a campfire in his mouth.
Darklings from the Midnighters series grow much, much stronger with age. Of course, they also get crazier with age.
In Tales of Kolmar, the Kantri grow throughout their lives, molting their armor every fifty years or so. The Eldest in that series, Shikrar, is over eighteen hundred years old and the largest of them, as well as a good fighter and the best flyer - though that last can't be attributed to his age, he became the best flyer and held on to that distinction from a much younger age. On their own Kantri reach about two thousand years before they die, which isn't discussed but it seems to happen fast. It's also noted that some grow "old before their time" and start to mentally slip; Shikrar suspects that another Kantri is one of these and guiltily wonders if he'll die in his sleep well before the two thousand mark, as these often do.
Inverted in David Wellington's 13 Bullets (and sequels). A vampire is never as strong again as it is its first night. They gradually grow more decrepit, requiring more and more blood to stay active. Older vampires are a threat because of greater experience and because their vampire progeny protect and feed them.
Aeriat in The Books of the Raksura grow larger and stronger with age; Moon has to inform his peers when they meet an elderly Islander that most "groundling" races don't do that.
In Robin Mc Kinley's Sunshine, this appears to be true of vampires, with some twists. Classically, in-setting, an old vampire is a master vampire, and very, very strong, but also the older he gets, the less he can endure sunlight, until even moonlight is crippling, which is why he surrounds himself with a gang of minion vampires. The main character, who develops a relatively Friendly Neighborhood Vampire (he still kills people, but cleanly, and not her) learns eventually that while power does naturally increase with age, the weakness to light actually increases with evil, and that while normally these increase in tandem, it's not mandatory.
Beauregard is stated to be in himself somewhat less powerful than his contemporary, Constantine, but while his body has broken down under his evil, his mind is horribly powerful. Due to evil. Meanwhile, he has a lot of mooks, which tends to tip the scale.
Live Action Television
Vampires work this way on Buffy the Vampire Slayer. Older vampires become stronger, tougher, and more demonic in appearance, and may pick up other powers, like Dracula's tricks. When Spike is first introduced Giles initially dismisses him as a big threat when he discovers Spike is scarcely over 100 years old (shortly after he discovers Spike's full history and reconsiders). Kakistos was noted as being an extremely old vampire and thus a bigger threat. His age meant he had lost most traces of a human appearance and a standard size stake wouldn't do the job, so Faith had to use a two-by-four to finish him.The Master (referred to as "the oldest vampire on record") was another vampire old enough to have stopped looking human, and had somehow gained the power to open the Hellmouth. The Master also took a larger-than-usual stake, dying when he was impaled on a broken table leg. And unlike other vampires who turn completely to dust when killed, the Master's skeleton remained intact. Until Buffy smashed it with a sledgehammer to prevent his revival in a ritual. Notably, the Master's inhuman appearance closely resembles that of the Turok-Han or "ubervamps" ("pure" vampires rather than former humans) of Season 7, leading some to speculate that he was the very first human to be turned into a vampire.
While age is a major favor in vampires' strength, bloodline seems to matter too. Spike, while not at all ancient, is by bloodline just 4 generations removed from the Master.
In Moonlight, Mick senses (or rather smells) that Lance is very old, who further reinforces this by jumping from a tall building (impressing even Mick) and surviving being burned (any part of a vampire that touches fire is normally instantly turned to ash). Coraline also somehow survived being trapped in a burning building and could move with a stake in her chest, which is normally impossible. By contrast, the 700-year-old Lola was pretty handily defeated by Mick, despite being able to move much faster than him.
In The Vampire Diaries vampires all become stronger as they age, although the difference can be overcome through numbers, surprise, anti-vampire weaponry, or other tactics. The oldest of them, the Originals, get a whole bunch of nifty powers and are next to impossible to kill. When they did manage to take one down, he would only remain dead as long as the magical knife that killed him wasn't removed, and his body remained indestructible.
Vampires from True Blood. Battles between vampires are always determined by how old each vampire is. Even the difference of about a year makes all the difference. They also seem to develop the ability to fly over time. However, their weaknesses also get more severe. A 2,000 year old vampire will burn up in the sun within seconds, whereas a younger vampire will take minutes.
Faeries also become more powerful with age. Their skills and power with photokinesis, telepathy, etc improve over the centuries.
Being Human: This seems to apply to vampires, ghosts and werewolves.
Vampires. While Old Ones still can be killed as easily as any other Vampire, they have a lot more "tricks" under their belt, with some such as Wyndham being able to casually enter without an invitation, something that would cause most Vampires to instantly begin to boil alive. Some physiological changes seem to occur with age as well. Mr Snow, the leader of the Old Ones, has developed a sickly pallor, rotting teeth and protruding black veins due to his advanced age.
Ghosts are also stated to get stronger with age. Most however fail to get that far due to losing their connection to the mortal world, leading them to simply fade away into non-existence.
Werewolves age normally, but they get stronger every time they turn. A werewolf who has been changing for years will be able to kill vampires with his bare hands.
Forever Knight worked this way. Lacroix was able to survive being impaled with a burning stake, and both Nick and Janette were also more resilient than many younger vampires. Also, Lacroix got his butt handed to him by his "vampire mother", who was a teenage girl when she was turned.
Religion And Myths
In Japanese folk thought, foxes (Kitsune) grow a new tail for every hundred years they live, with a proportional growth in power, to a maximum of nine, at which point they're pretty much Physical Gods.
In fact, there's a whole subgroup of Youkai / Obake who were former ordinary objects or animals who acquired supernatural powers and sentience after being used/living long enough (usually about a century).
Dungeons & Dragons has this happen to many creatures. Vampires, dragons, liches and others tend to grow more powerful as they age. The Ravenloft setting is especially keen on doing this with The Undead. Pictured above are red dragons. For the record, the second largest one is an "adult". The top one is an ancient.
Warhammer and Warhammer 40,000 contains plenty of examples, and though many are due to the "more experience" version many others fit this trope.
Vampires in the Old World of Darkness game Vampire: The Masquerade are stronger with age in two ways: experience and Generation. Older vampires are more experienced (obviously), have more and stronger Disciplines than neonates, and have influence over vampiric and human society. A vampire of lower Generation is closer to the blood of Caine than a 13th-Generation neonate (the game's "default" new player characters), increasing their stat caps and allowing them to spend more Vitae faster.
The successor game, Vampire: The Requiem, subverts this with its Blood Potency stat. Like Generation, higher ranks of Blood Potency allow a vampire to spend more Vitae and have higher stats, but can't regain Vitae from animals and eventually humans. Instead of being a simple "I'm stronger than you" score, high Blood Potency invokes a psychological need to enter torpor, during which the vampire's Blood Potency drops and he forgets his experiences (the so-called "Fog of Ages"). Ergo, no Kindred stays stronger with age, since they depower while in torpor and their memories become faded dreams. Methuselahs, however, do not suffer the Fog of Ages.
With the right Coils of the Dragon, its possible to utterly avoid the increased blood thirst that comes with age. Meaning in a few centuries, we might have Blood Potency 10 blood gods running around that can still feed on humans rather then other vampires...
Mummy: The Curse, however, is an inversion of this trope — a mummy rises at the peak of their power, but it quickly drops a rank and then starts to level out until it's at its weakest, which is when the mummy needs to go back to rest.
In a fantasy-steampunk RPG Wolsung, trolls fall under this trope without exceptions. When they are about 50 years old, they start to burn out mentally, fall into fits of rage, and at some point they hulk out. Permanently. From this point, they become larger, more resilient and feral with age... and nobody ever checked just how old they can get. Usually, their family or the authorities will put them down shortly after the onset of this freakish senility.
It's less pronounced with troll women, who don't lose so much of their brains - just their morals. They are more likely to serve you arsenic tea and cyanide cookies than to rip you limb from limb. At least in the first stages of senility. Then they get worse.
This "old troll syndrome" is the reason why most well-mannered trolls are expected to commit suicide when they notice the first signs of old age, to prevent a scandal (Victorian morality in practice). Those who are unable to perform the act usually depend on their next of kin to assist them once the transformation starts.
The potential for power of Exalted is tied directly to age, with caps placed on their highest potential Essence based on how long they've lived (although there are a few magics that can break this). The highest levels of power are only available to Exalted who are more than a thousand years old.
Due to the Great Curse, this also means that the ones with access to the high Essence charms are also the most likely to be utterly insane, driven mad by the Curse, and rather prone to even greater acts of madness while in Limit Break.
Dragons in Magic The Gathering. Dragons only get bigger, stronger, and smarter as they age. The last Elder Dragon, Nicol Bolas, is an incredibly dangerous villain who is "Dominaria's most ancient evil." They apparently can die of old age eventually, since one of Nicol Bolas' goals was to regain the immortality he lost when his Planeswalker Spark was weakened by the Mending.
Fallout 3 Super Mutants grow stronger (but not smarter — the opposite is implied to be the case) with age. Super Mutant Brutes are younger and weaker than Masters, who are weaker than Overlords, who are weaker than Behemoths, who are the oldest. Not that this particular trait is not (explicitly) shared with their west coast counterparts.
In fact, in Fallout 2 the Super Mutants of Broken Hills are said to be slowly going weak and senile. This is probably due to being infected with a different strain of FEV (found in the Mariposa Military Base) than the mutants in the Capital Wasteland.
Even the Capital Wasteland Mutants don't all follow the rule — it is heavily implied that Fawkes, one of your companions, was one of the first East Coast Super Mutants, yet he's still a regular Super Mutant.
The asari in Mass Effect are said to show this, at least with regards to their biotics, which grow in power as they reach the matriarch part of their life cycle.
Kaidan Alenko suggests that this is not restricted to asari, noting the increase in his own biotic abilities over the previous three years.
A few of the legendary Dragon-type Pokémon count, but the very old Rayquaza stands out the most. Although it had lost nearly all of its teeth through the decades, it still flies and battles as if it hasn't aged a bit. Not to mention its high attack stats.
The Creation Trio have special mention here, since they literally created the universe itself and still live on to present day. Although, that's probably because two of them are literally gods, while the third one is undead.
Dragons in Dragon Age only get more powerful with age. The Darkspawn also demonstrate the same is true of them, with a mini-boss Hurlock Vanguard in the Deep Roads called "Ancient Darkspawn."
And then, in Dragon Age II Legacy, there's Corypheus, the most ancient Darkspawn (or at least, one out of half a dozen of them).
The same could be said of the Grey Wardens, due to the Darkspawn Taint within them getting stronger over time. However after 30 years, they gradually start to go insane as the Taint turns them into Ghouls.
Some of the monsters in darkSector are stated as getting larger and stronger with age. Just before a boss fight, an ally warns you, "This one is very old!"
Vampires in The Elder Scrolls grow more powerful as they age. Vampire Ancients are the oldest and strongest vampire mooks/bosses, and Vampire Lords of Skyrim, who are the first and oldest vampires of their entire clan and received their vampirism directly from the evil god Molag Bal, are the strongest named vampire characters.
In League of Legends, the Voidlings created by Malzahar grow more powerful every six seconds. Eighteen seconds after they are created, they just die.
Nym, from the Star WarsStarfighter series, is a Feeorin, who are specifically noted to grow progressively stronger as they age. And since they can live as long as four hundred years, that's quite a lot of room for growth.
Liir from Sword of the Stars have this; the older they grow, the larger they get and the more powerful their psionic abilities become. The only thing limiting their size, and eventually causing their death, is the Square/Cube Law. Of course, some didn't like that last bit, preferring to enslave the younger ones to make them build spacesuits for them, so they could live in space and remove that last limit on their immortality. Very few remain of those who did this, but just one can wreck whole armies.
Legacy of Kain: Vampires "evolve" over time, occasionally entering a cocoon-like state and emerging changed; Typically stronger and with new abilities, as well as less human. But Kain's spiritual and mental corruption caused his descendents to eventually degenerate (or something similar). It's implied that a vampire's evolution conforms to his personality; Vorador's chin horns used to be a similar beard, human Rahab's armor had a seahorse painted on it, and Raziel told Zephon the latter's final form is a true representation of his soul. It's revealed in Soul Reaver 2 that some changes, like the typical three-fingered hands, are the turned vampires becoming more like the originals.
In Guilty Gear, Slayer is a Nightwalker who is several hundred years old, the original founder of the assassin's guild, and one of the most powerful characters in the series. It's heavily implied that he's holding back on the whole cast; even if you utterly destroy him in a fight, he'll just lie on the floor with his head in his hand, casually chilling out.
Also, JamKuradoberi, who is told after fighting Slayer that given enough time, she'll end up surpassing him.
Immortals from El Goonish Shive continue to get older, smarter, stronger, more bored and less sane until the point comes where they basically become People Of Mass Destruction. To prevent this, they voluntarily undergo a kind of ritualistic death/rebirth cycle every couple of centuries to lose most of their power and memories so they can start over and keep things interesting. A significant portion of the current plot is being driven by Pandora Chaos Raven, an immortal who refuses to let go of her accumulated power, and seems to be approaching Eldritch Abomination territory.
Forget people. Gustave has been known to attack and eat hippos. Bear in mind that a full-grown hippopotamus is more than capable of killing an average-sized Nile crocodile. Gustave being able to hunt down what is considered to be the most dangerous animal in Africa says a lot about his strength.
Gustave is known to have wandered inland and snatched people without apparently caring if someone fires a submachine gun at it. His hide could be so thick by this point, he might not even notice the bullets bouncing off his scales.note It's clear why crocodiles are though to have inspired the dragons of myth.
Trees, sequoia in particular.
Lobsters are a perfect example. According recent research, a lobster does not weaken or slow down with age. In fact, it becomes more fertile as it gets older compared to younger lobsters. Barring injury, disease and capture they can live on indefinitely, reaching impressive sizes. All this is attributed to telomerase, an enzyme that repairs DNA sequences of the form "TTAGGG". This sounds cool until you realise that theoretically, there could be centuries-old lobsters the size of houses scuttling around on the ocean floor. Or not, since they'd have to eat.
There's serious scientific research to allow us to do the same. The only problem is it's a double-edged sword. Telomeres wearing down puts an upper limit on cell multiplication, but trying to take away cellular regulatory systems can result in immortal cells that can multiply indefinitely but also grow out of control, turning into cancer.
Reptiles in general. Most animals reach a certain size and stop growing. So long as a reptile doesn't get killed or die by other means it just keeps getting bigger and bigger as it ages. Of course, they still die of old age at some point.
Sharks. It is believed that some great whites still swimming the seas today are centuries old. A great white shark is believed to keep growing until it's killed, and since any that die of old age are likely to get eaten before humans can look at themnote It's difficult to get a captive great white shark to eat, so few attempts are even made at capturing them anymore. A handful of aquariums periodically capture a juvenile great white, but they're invariably released back into the wild after a few months to ensure their survival. it's anyone's guess how long they live.
Some species of whale. While most of the big whales live 60-70 years, bowheads are believed to have very long lifespans. Whales captured by native whalers off Alaska in the 1990s were found to have harpoon heads embedded in their blubber which were last used by native Alaskans in the 1800s. A whale killed in 2007 had the tip of explosive harpoon head deep in its blubber that had been manufactured around 1890, indicating it had survived a previous hunt at least a century earlier.
Most animals, really. Mammals, with their short stage of rapid growing, limited reproductive life and only two sets of teeth are the exception, not the rule.
There was a koi fish named "Hanako", who passed through several different owners. She lived to be 228 years old! (For reference, the average koi lifespan is about 50 years, although there are plenty that live longer. To date, none are known to have lived as long as Hanako, however.)