A few Digimon. In particular, Tyrannomon even has the Godzilla-ish back spikes, and his larger, darker Palette Swap, Dark Tyrannomon, was once used for a very Godzilla-evocative scene when the battle was taken into the human world. Powers That Be resisted the urge to use the distinctive Godzilla roar, though.
The series has an example that involves Espada #0 Yammy Llargo, whose release 'Ira' transforms him into a monstrous Kaiju.
Gillian-class Menos (and Arrancar formed from them) are probably big enough to count, too, even if they are considerably weaker.
The closest we've got to a battle of two Kaiju is the fight between captain Sajin Komamura and arrancar Choe Neng Poww. Powws Resurrección Calderon turns him into a whalelike giant, where as Komamuras Bankai Kokujō Tengen Myō'ō summons a giant in full samurai armor. Then Komamura activates the Dangerous Forbidden Technique
In the CLAMP series Cardcaptor Sakura, Touya's pet name for his sister is "Kaiju", which is usually followed by Sakura shouting about how much she isn't one, complete with monstrous stomping about the house. Which naturally only adds to Touya's argument that she is a noisy kaiju.
Franken Fran had a massive human-like Kaiju that came from the sea and seemed intent on attacking an island town. Turns out that it's just a girl whose wish of living with the whales was granted by Professor Madaraki. She's just there to find her mom so she could give her the great news that she's now pregnant. Happy end!
Pokémon: Legendary Pokémon are anywhere from "extra-large" to "titanic" in size, especially if it's a more "beastly" Legendary (Groudon, Rayquaza, Giratina). Non-Legendary examples include the cliff-sized Dragonite in "Mystery at the Lighthouse" and the skyscraper-tall Tentacruel in "Tentacool and Tentacruel".
All members of the Heroic Tribe in Heroic Age are essentially GIANT SPACE MONSTERS. Which destroy planets on a regular basis.
The largest summoned animals in Naruto fit the bill in terms of size. The giant serpent is even named Manda after the Godzilla beast. There's also the Bijuu: 9 giant monsters, at least one of which was once referred to as a natural disaster, which is far more in theme with the iconic Kaiju.
Lampshaded by Guy, when Kurama and Gyuki fight the five other Bijuus Matatabi, Isobu, Kokuoh, Saiken and Chomei.
Guy: "It looks like the battle of Kaijus!"
In Mahou Sensei Negima!, the Sacred Beast of the Hellas Empire recently started attacking a gigantic shadow monster, causing Haruna to start squeeing about kaiju battles. And Lovecraft.
Many larger Capture Beasts in Toriko fit the role. The Four Beasts and their master beast fit this especially. More powerful beasts in the Gourmet World make Godzilla look small.
In Shinzo, Enterrans are basically mons that populate the earth After the End. They don't get ginormous... usually. One Big Bad has as The Dragon an actual three-headed dragon named Grendora. Grendora is positively enormous, shoots ice blasts, and uses canned Godzilla roars.
Many of the gigantic monsters from Yu-Gi-Oh! count, especially the ones who are extremely powerful in-universe. For example, Exodia, the Egyptian Gods, the Great Leviathan, the Sacred Beasts, the Earthbound Immortals, etc.
One "Metropolis Mailbag" episode featured Superman's annual New Year's help-by-mail tradition interrupted by a fight between a gigantic Metallo and the new Toyman, a Japanese kid with a Super Robot. Between performing his tasks and trying to keep the battle from escalating, he also had to deal with several giant monsters awakened by the fighting: a massive butterfly, a Gorilla-Whale (A literal translation of Godzilla's name), and of all things, a giant purple Pikachu.
Fin Fang Foom of Marvel Comics, a giant Chinese dragon. Depending on the Writer, he's usually said to be an alien, a member of the race who invented the Mandarin's power rings. Foom is a holdover from when Marvel published monster comics as a major source of revenue. Today, Marvel's Monster Island houses lots of Kirby-designed and inspired Kaiju. Some others who show up in modern continuity are the tree-like alien Groot and the lovable giant ape-monster Gorgilla. Big Hero 6 and other Japanese superhero teams within the Marvel universe apparently spend a lot of time defending cities from giant monsters.
Marvel briefly had the rights to publish Godzilla comics, and featured him as part of the Marvel Universe. As with Marvel's otherlicensedproperty titles, he accrued a supporting cast of friends and enemies whom Marvel does own and who still pop up once in a while, such as Yetrigar the giant yeti, a giant robot named Red Ronin, and a Mad Scientist named Dr. Demonicus who specializes in mutating animals into Kaiju.
During Walt Simonson's run of The Mighty Thor, Fafnir the dragon sure had the size to qualify.
Batman: Gotham After Midnight, a very bizarre miniseries, featured Bat-foe Clayface devouring people whole and growing into a gigantic mud-monster... which the Dark Knight fought with a Bat-mecha he had built for just such an occasion. Crazy-Prepared, indeed...
The Planetary team discover the remains of various ersatz kaiju on Island Zero.
Exiles had the Monster World arc, which envisioned Curt Connors, Bolivar Trask, Tony Stark, and Hank Pym as a team of Action Scientists fighting Kaiju in a transforming mecha. They fight it out with Fin Fang Foom in Japan at the end of the arc. It was awesome.
Avengers: The Initiative: When the new 3-D Man is sent to a superhero team in Hawaii he finds out one of his missions is to protect the state from the occasional kaiju that wanders over from Japan.
Fire Breather. Duncan's daddy, Belloc, actually calls himself king of the Kaiju and wants his son to one day take his place.
The comics mini-series Gigantic combines this with Truman Show Plot. The first kaiju on Earth, Gigantic, is trying to escape the mega-corporation that controls him, and the entire earth, having built it from scratch for a TV station.
The very first issue of Plop! had a story about "Kongzilla," a beast with the top half of a giant ape and the bottom half of a giant lizard.
The Warren Ellis miniseries Tokyo Storm Warning is an homage to kaiju manga and anime, with an eye turned toward realism as the robots and kaiju cause massive property damage and send literal waves of kaiju blood washing away civilians.
Dan Brereton-illustrated Giantkiller was about an invasion of California by colossal, extradimensional monsters who turn the state into an extension of their own world. It featured 25 different giant Kaiju plus a half-human hero to slay them - one for each letter of the alphabet.
Gold Digger featured an island inhabited by giant monsters, a result of the unusual emanations of the island itself. The native tribe, the Ooshoosh, also adapted... the women, while being born as normal-sized babies, grow unusually fast into 40-foot monster-slaying giantesses who are very protective of their normal-sized men. Well, mostly normal-sized, that is.
IDW has been publishing Godzilla comics since 2010. Unlike other companies before them, they also have the rights to most of his supporting cast.
Discovery Channel aired a doufiction story entitled Alien Planet, loosely bases on Wayne Barlowe's Expedition. One of the freaky beasties we see is the Emperor Sea Strider, a creature dwelling in the Amoebic Sea that stands 620 feet tall- that's three Godzilla's standing on each other's shoulders, or as high as London's BT tower.
The Future Is Wild had the Toraton, a creature from the Bengal Swamp living 100 million years in the future. It's basically a giant, shell-less tortoise that grows 15 times as big as an elephant and weighs a whopping 120 tons.
The Pony POV Series has Queen Tiamat, the Dragon's ruler and Mother Goddess. Normal adult dragons are Kaiju, Tiamat dwarfs even them, being large enough to blot out the sun when standing at her full height and immensely powerful. She joined the fray herself during the Dragon-Hooviet War and proceeded to leave half the empire in flaming ruin, willingly stopping just short of the capital. The Hooviets weren't able to even hit her, let alone do any lasting damage.
Cloverfield is a deconstruction of all kaiju attack movies, reminding people that Kaiju has its roots in the Disaster film and how terrifying, deadly, and incomprehensible such an attack would be to an average citizen as it did in the first Godzilla film.
Insectosaurus of Monsters vs. Aliens, down to having the same backstory as Godzilla, though generally being a homage to Mothra.
The gigantic alien probe-robots also.
In an inversion, Lucas from  is a normal human kid, but wreaks similar wrath and destruction upon a hapless ant colony.
REPTILICUS! The giant goop-spitting snake-dragon that destroyed Copenhagen!
THE GIANT CLAW! The flying battleshipGiant Antimatter Space Buzzard from 17,000,000 B.C.!
Street Fighter has a tribute to these, with Zangief and E. Honda duking it out in a model city.
Referenced in Deep Rising, at the end of which something unseen but HUGE moves toward the beach and the survivors, knocking down trees as it approaches. Not to mention its own multi-armed, lamprey-headed octopus with mouths at the end of each arm. Its head fills a ballroom and its tentacles can reach throughout an ocean linear.
Thunder of the Gigantic Serpent, a japanese kaiju flick and one of Godfrey Ho's flicks that don't involve ninjas, has one of the largest snakes in cinema. It's head being bigger than a car when it gets big enough.
The Blob can be seen as a Blob Monster taken to this level as it grows larger. The 1980s Remake's climax is a full on Kaiju rampage.
A lot of Blob Monsters get Kaiju like as they get bigger.
Gappa: The Triphibian Monster fits the bill.
Yonggary: the Monster from the Deep and its remake Yonggary are basically Korean Godzilla-knockoffs. The later film has it fight another Kaiju, named Cykor.
Space Amoeba features an extraterrestrial parasite that possesses the bodies of various sea creatures(a cuttlefish, a stone crab, and a rock turtle), turning them into giant kaijus.
Aside from King Kong, there are other giant ape Kaiju. These include The Giant Peking Man, Konga, A.P.E., and King of the Lost World.
It Came from Beneath the Sea features an Octopus of Kaiju Proportions. Several other films (usually titled things like Octopus and Octopus 2: River of Fear) feature similarly large giant cepholopods, but aren't as good as Ray Harryhausen's.
The title monster from Supercroc is a Kaiju-sized Crocodilian, with appropriately thick armor.
Iron Golem/Minotaur in Pulgasari isn't too big, but given its attacking medieval villages, it fits the bill. Notable for being from North Korea, and eventually banned there.
An American Direct-to-Video film called The Adventure of Galgameth reset it in Medieval Europe, but has the same plot as Pulgasari, right down to the eponymous monster's weakness to salt water and growing by eating iron and its derivatives.
The Daimajin series' eponymous monster is an ancient demon-god. It too battles medieval forces, but with a stone body and mystical powers. It also exists to punish the wicked—but has unreasonably high standards. So, each time after it frees the oppressed villagers from the evil warlord/king, it goes on to attack them.
The space monster Guilala from The X From Outer Space is one of the most bizarre Kaiju to have its own films.
Hot Fuzz seems to pay homage to this genre in part of its climax, with normal-sized humans Nicholas Angel and one of the villains having a brutal fistfight in a model village.
The protagonist from Big Man Japan might be considered one but his giant monster foes certainly are. Unlike most Kaiju, though, they tend to be somewhat humanoid, and sometimes don't even fight and merely humiliating the protagonist.
Humongous Mecha film Pacific Rim has an entire army of these, even named as such by the humans, rising out of a dimensional portal in the Pacific to launch an extinction campaign on the human race. This is also one of the few non-Japanese films to use the actual word "Kaiju" to describe the creatures, to the point where less well-informed fans think that the movie invented the term.
Pulgasari may very well be the only notable example of this to come out of North Korea. Toho's special effects team even helped out, with the eponymous monster, which resembles a cross between Godzilla and an ox, being portrayed by Godzilla suit actor Ken Satsuma.
In The Silmarillion, when Morgoth unleashes the first winged dragons during the Final Battle, they are led by Ancalagon the Black, bred specifically to be the greatest dragon to ever live. He could certainly fit the Kaiju bill: his approach was heralded by a firestorm, and when he died his falling body crushed three of the highest peaks on Middle-Earth which served as Morgoth's Evil Tower of Ominousness. The only things known size-wise about Ancalagon are that when he was finally slain, his downfall destroyed the Thangorodrim. From what we can read in the books, the Thangorodrim is a three-topped mountain with an assumed height of 35,000 feet and a diameter of 5 miles. Considering that the only thing that Tolkien wrote about Dragonmagic was the power of deception, we can probably be sure that the mountains were destroyed purely by his size and weight - so that makes Ancalagon big enough to - in Real Life terms - destroy Mount Everest by simply falling on it. In short: Ancalagon the Black might not just be the biggest Dragon in Tolkien's works, but might even be one of the largest dragon in fiction.
Cthulhu and his children (Ghatanothoa, Cthulhu's first born, actually has a character directly based on it in Ultraman Tiga).
Agog Press' Daikaiju! anthology is built around these, and features a number of really weird ideas. How weird? Groundsurfing on the shockwaves made by kaiju's feet as they walk around.
The avanc from The Scar is an unusual variant, as this gargantuan marine creature didn't destroy a city by stomping through it, but by dragging the floating city of Armada to its doom in the eponymous Scar.
At the end of Unseen Academicals, Ridcully informs Ponder that a seventy-foot chicken has broken out of Brazeneck College's Higher Energy Magic building and is rampaging through the streets of Pseudopolis.
Great A'tuin and the four elephants riding its shell would qualify, if they weren't supporting the world rather than stomping all over it.
And an earlier book had a giant creature from the Dungeon Dimensions steal the form of a famous actress, escape from the Silver Screen and go on a rampage across Ankh-Morpork and climbing the UU's Tower of Art carrying a screaming ape in an inversion of King Kong.
Something inconceivably huge and six-legged walks across the highway in Stephen King's novella The Mist, nearly stomping the protagonists' SUV. Its full size is not specified, as its body is so high that it's obscured by the fog.
Gojiro by Mark Jacobson is a deconstruction of Kaiju monsters told from the point of view of the monster Gojiro and his human partner Komodo as they attempt to bring about world peace and prevent the testing of a next-generation nuclear weapon.
In The Iron Man, the children's novel by Ted Hughes that was the basis for The Iron Giant, the Iron Man confronts an alien dragon creature somewhat smaller than Australia. While this plot point wasn't featured in the movie, it was featured in "The Iron Man; The Musical", a concept album by Pete Townshend of The Who inspired by the novel.
The stavanzer, or thunder-eater, from Icerigger is a slug-like herbivore over a hundred meters long, and it's mentioned that such creatures have been known to destroy tran settlements.
Monster Blood's title substance typically makes things grow to giant size, but the second book took it a step further when the climax involved the protagonist eating monster blood to fight a giant hamster eating his school. True to kaiju form, this involves a giant wrestling match.
The genre is parodied by a series of childrens books, one called Dogzilla and one called Kat Kong.
In the League Of Magi stories, Shahmeran's alternate form is a massive serpent.
Live Action TV
Abbadon from Torchwood is a giant life-sucking daemon which, when released, goes on a rampage in the streets of Cardiff.
Rampant in Super Sentai as well as their American import Power Rangers; less common in Kamen Rider, where the monsters tend to stay small-sized. (Except Kamen Rider J.) note There's actually a generic term in Japan for Monster of the Week types in the spandex-versus-People in Rubber Suits genre - a kaijin is like a kaiju but smaller and more humanoid. Of course, as special effects grow on television but traditionalism and Narm Charm rules in monster movies, there are creatures who are considered kaijin because of the show they're on that are more monstrous than◊ creatures who are considered kaiju because of the films they're in. So, in real-life terms, a kaiju is a movie giant monster and a kaijin is a Toku series' Monster of the Week.
Kamen Rider Hibiki has a lot of gigantic Makamou beasts, and in Kamen Rider Den-O, there are Imagin capable of going One-Winged Angel, becoming giant beasts called Gigandeaths. In Kamen Rider Wizard, a Phantom who hasn't hatched from its host yet appears as a monstrous beast within the mind of the victim, which must be battled within the mindscape by Wizard. The franchise is actually no stranger to giant beasties, and not a Humongous Mecha in sight! However, the Riders' vehicles are sometimes very weapon-laden. Interestingly, Wizard has to use his own Inner Phantom, Dragon, to fight the Inner Phantoms, his Second Rider Beast having to do the same thing.
Another story called The Seeds of Doom features an alien plant called a Krynoid, which eventually grows to a size of several tens of feet tall. The Doctor says it will max out at about the size of St Paul's Cathedral (at which point it will release thousands of seeds, dooming all animal life on Earth).
Then there's the Robot from the serial, Robot, and the Cyberking from the 2009 Christmas special.
The Kardas Dragon, Tahtorak, Kanohi Dragon and Zivon from BIONICLE. Fittingly, the Kardas is one of the largest sets released, while the Zivon is a combiner model made up of six sets (the other two are fan-built models). And yes, some of them did clash and wreck cities at various times. You may also count the Ancient Sea Behemoth and the Kraawa, the latter of which is a Size Shifter beast with no known size-limitations.
Doctor Steel's song "Atomic Superstar", featuring the original Kaiju, Godzilla.
Surf rock revival band "Daikaiju" takes cues from many old Kaiju and sci-fi films. Song names include: The Trouble With Those Mothra Girls, Son of Daikaiju, Farewell to Monster Island, etc. The music itself is pretty damn good
Rapper MF Doom's alter ego King Geedorah. The album, Take Me To Your Leader, also features a number of rappers under various Kaiju names (Rodan, Gigan, Jet Jaguar etc).
"The Cockroach That Ate Cincinnati"
"Godzilla Ate Tukwila" by Dave Phillips. (Tukwila is a small town in Washington state; in the course of the song, the Big G eats several others as well.)
Norse Mythology brings us Jormugandr, the World Serpent. Enormous reptilian beast that will rise from the sea surrounding the world and has deadly breath. Sound Familiar? Regular monster, no way. You wanna take this down, your name best be Thor, god of thunder. Not to mention the giant wolf Fenrir.
Classical Mythology has a few of these as well. Part of this was due to the idea that the Heroes of their myths were thought to have been giants themselves, standing roughly 3-4 times the size of modern men with the Gods and Titans being roughly that scale to them. But to bring up specifics, the titan Typhon with his multiple heads and burning body definitely counts. The original Chimera was treated as such, as were many of the monsters defeated by Hercules (Nemean Lion, Hydra, and the taming of Cerberus). The monsters Scylla and Charybdis also fit the Kaiju mold, being unstoppable by mortal men.
Many of the most dangerous Giants and Dragons were essentially prototype Kaiju.
In Hindu Mythology, there's many a Rakshasha and Naga of immense size. Of note are Kumbhakarna, who was a giant even among the monstrous Rakshasha. His brother, Ravana, for his many heads and hands. Then there's Ananta-Sesha, a world serpent of a much more benevolent bent.
Then there's Mada, an Asura that can make itself so large that it's capable of swallowing the universe.
Some accounts of the Garuda depict this gigantic bird as being so large, it could pick up Godzilla and carry him off.
From Abrahamic traditions and The Bible, we have the lords of the animals: Leviathan, Behemoth, and Ziz. One's a giant aquatic dragon, the other an immense beast with a massive tail, and the last a giant bird.
Older Than Dirt: From the mythology of the Babylonians, there's the monstrous Eldritch Abomination goddess Tiamat and her progeny. Mesopotamian myth also involves gigantic dragons.
There's a Native American legend (which nation is unknown) involving a giant rattlesnake several hundred miles long.
Garfield usually mocks bad horror movies when it goes pop-cultural, but on one occasion the title character saw a news interview with "a prehistoric monster who rose from the depths of the Earth to stomp on Tokyo, and has written a book about his experiences (of course.)"
In Calvin and Hobbes, Calvin is a big fan of Japanese monster movies. He imagines himself as Godzilla on two occasions: stomping a sandbox version of Tokyo, and rising from the watery depths of his bathtub to blast Megalon (his mom).
In a similar vein, this classic American political cartoon◊ depicting the Standard Oil Company as a giant evil octopus, with its arms moving in to strangle the people and the government. This symbolized the perception of Standard Oil (and by implication other large industry trusts) as harmful monopolies.
"Kaiju" is a template (see Dragon #289), enabling the DM to turn any Animal, Magical Beast or Vermin in the Monster Manual into a fifty-foot armour-plated monstrosity capable of destroying TokyoNakamaru.
Older Than They Think, as the old Basic/Expert/etc version of the rules had a proto-template for super-sizing normal monsters over a decade before that issue came out. They also had critters that qualified as this trope right out of the box, like the earthquake beetle.
The original Oriental Adventures supplement introduced a number of creatures called "Gargantuas" that were Captain Ersatzs of Godzilla, King Kong, and Mothra.
An adventure for the Oriental Adventures campaign setting, Test of the Samurai, featured a gigantic psychic monster called a "Krakentua", which is best described as Cthulhu, sans wings, in a kimono.
No discussion of giant monsters in D&D is complete without mentioning the legendary Tarrasque. Only one exists on any given world; this reptilian monstrosity awakens every century to destroy everything in its path, devouring all life and reducing the countryside to rubble, and is completely unkillable without resorting to godlike magic.
In addition, if you DO manage to kill it, the Princes of Elemental Evil will just create a new one.
In Pathfinder, the Tarrasque, while still unique, is one of a whole family of unique kaiju created by the apocalypse god Rovagug. Which is itself an unbelievably gigantic insect-Eldritch Abominationimprisoned in the molten heart of the world in a cage whose bars are strong enough to hold it in, but wide enough to allow its comparatively tiny and ineffectual spawn to escape.
Pathfinder also includes the creatures aptly called Kaij, colossal creature from the Valashmai jungle, including one that is an undead alien bioweapon. The Oliphaunt of Jandelay also counts, being one of the most powerful creatures in Pathfinder, and sharing some traits with Kaiju.
The Spelljammer setting has Witchlight Marauders, which function as both this and Eldritch Abominations. That's the Primaries at 200' to 500' long (Secondaries are still massive, but much smaller, derivatives of the Primaries at 20', and Tertiaries are human sized at 4' to 6' and still deadly), which were created with the explicit purpose of stripping life-bearing planets down to the bedrock. For true cosmic horror, there are the Space Marauders at over 1000' long, which create Primaries and drop them onto planets and function as living spacecraft as well.
Spelljammer also featured a world crawling with Tarrasque-equivalents... with the twist that on that world, and only on that world (it was probably something to do with the atmosphere — the implication was that this was the homeworld of the Tarrasque) they dropped the periodic omnicidal rampages for being docile lithovores.
Exalted has its share of giant, rampaging monsters. Most of these are behemoths, created either by the Fair Folk for use in their reality shaping battles, or by the Primordials, for shits and giggles. Occasionally, an elemental dragon will ascend to such a level of spiritual development that it goes insane. Also, elder Lunar Exalted can use their Voluntary Shapeshifting to change into an incredibly strong monster that dwarfs cities.
One of the more distinctive behemoths of the setting is Juggernaut, Mask of Winters' undead citadel-beast that aided him in sieging Thorns.
And then you've got the hekatonkhires, which are often what happen when behemoths die. One of them, Vodak, ate a city.
The game Gammarauders featured gigantic cyborg animals and dinosaurs with a variety of weapons sprouting from their bodies. Few things are more terrifying than a giant cybernetic Penguin waddling toward you, wrecking buildings as it comes.
The Creature That Ate Sheboygan, a wargame from SPI, is about the title city being attacked by a giant monster. One player defends the city with the National Guard and the other plays the monster.
Star Fleet Battles includes a number of space monsters of various types (some living, some not), mostly for solo scenarios. One such scenario pays homage to the above game with the subtitle "The Creature that ate Sheboygan III".
Warhammer 40,000. The larger Tyranid creatures, known as Biotitans, definitely qualify. The Tyranids created them in response to the Imperial Titans.
Chaos occaisionally throws this trope into play. While it mostly only brushes this trope in the form of Daemon Princes and Greater Daemons, it sometimes comes out with a really big Daemon Prince or Greater Daemon. They do have the occasional variance, one of them being a giant Chaos spawn named Jibberjaw. While they do have kaiju, Chaos most often plays on the opposite spectrum of this family of tropes, as they sport super-heavy vehicles, most notably traitor titans, and the occasional super-heavy daemon engine, many of which arguably fit both tropes.
ChampionsHero System Bestiary. The Hach-U-Rui are giant Japanese reptiles (minimum of 100 meters tall) that can survive hits by howitzers and may have an energy breath weapon. In short, they're the Champions equivalent of Godzilla.
BIONICLE: Vezon's pet dragon Kardas, a transformed version of a giant mutated spider. With the ability to create concussive blasts. To quote "Who's my favorite weapon of mass destruction, then?"
Hero Factory, Bionicle's successor, has come out with the Pacific Rim -inspired "Invasion From Below" storyline, which involves giant kaiju-themed beasts that, among other things, rip out streetlights and communications antennas and rampage around the city.
From 1961, The Great Garloo!
Resistance 2 has the Leviathan, a giant monster that roams the flooded streets of Chicago.
Spoofed heavily by the Lungfishopolis level of Psychonauts: one mind is portrayed as a city of tiny lungfish-like creatures, meaning that Raz is gargantuan compared to them. Due to his distinctive headgear, the citizens immediately nickname him Goggalor. The Boss Battle of the level is the Villain with Good Publicity kaiju, who's hailed as a hero to protect them from "Goggalor" (and a Shout-Out to Ultraman)
Destroy All Humans! 2 has the "Kojira Kaiju Battle" mission, a Godzilla parody complete with someone screaming "Kojira! Aieeee!", atomic breath, and those weird anti-Kaiju tanks common in Godzilla films. Naturally, it takes place in Japan.
X-COM: Apocalypse has the Overspawn, giant aliens dropped by the Mothership for the sole purpose of rampaging all over the cityscape. They're actually pretty weak since they're usually up against the best of X-COM manufactured vehicles and weapons by the time they appear. Some players just leave them alone since they have a tendency of accidentally killing themselves when they get too close to a building they knock over.
Speaking of rampaging, the characters you use in the Rampage series of games.
The Dragon Aspects are huge. Fore reference: The tallest playable race in the MMO, the Tauren, have males that are around 8'6. A Tauren player barely comes up to the top of Alexstrasza's claw. However, Deathwing, as shown in the trailer for Cataclysm, and the game proper takes the cake. He's described as "airliner big". Conservative estimates put him smaller than a Boeing 747 (specifically about 200ft long, 91ft tall, and a wingspan of of 400ft), maximum estimates put him on the scale of GODZILLA from the new movie.
Galakrond, the "progenitor of dragonkind" takes this Up to Eleven. He's so massive, that his full body isn't even seen in game, just parts of his skeleton. The artwork◊ of him from the novel Dawn of the Aspects shows that he utterly dwarfs the Proto-Dragon forms of the Aspects. For scale purposes, that's a small mountain below his right foot on the bottom left of the picture.
Kyogre and Groudon of the Pokémon games. Sootopolis was the unlucky city that had front row seats to their coming. Heck, when the time came for Pokémon Special to adapt the Ruby/Sapphire games, the artist said that he wanted to recreate scenes from his favorite monster movies when he was drawing the volumes that involved those two's disaster-filled awakening and eventual battle. Following them are Palkia, Dialga, Giratina, and Arceus, who all possess semi-godlike powers that cam tear the very fabric of reality. Meanwhile, Tyranitar, Hydreigon and Volcarona seemed to have been inspired by Godzilla, King Ghidorah, and Mothra respectively.
The WEAPONs of Final Fantasy VII are quite distinctly Kaiju, right down to incoherent roars, being vaguely humanoid, coming from the depths of the ocean, attacking major population centres and making craters on the main map screen when finally killed.
Age of Mythology's expansion brings Titans to the battlefield. They're huge, they can trash a city on their own, and it takes a ton of firepower to bring one down. Don't let your enemy summon one.
Spore gives us Epic Creatures which you can encounter early on in the creature stage. Later on in the Space Stage, you can make your own and send them to destroy cities for you!
The Elder Scrolls IV: Oblivion has at least two. First and foremost is Mehrunes Dagon, Daedric prince of destruction, and Jyggalag, Daedric prince of order. Although Jyggalag is the smallest of the two, he is taller than the city walls and is very powerful.
Crush, Crumble, and Chomp! gave the player four cities to destroy (Tokyo, New York City, Washington DC and San Francisco) and six monsters to destroy with (along with the ability to make your own monster).
Being a spinoff of Ultraman, Kaiju Buster Powered naturally has plenty of Kaiju. However as it's also heavily inspired by Monster Hunter, said Kaiju are more then capable of being taken down by humans with swords and energy weapons.
Parodied in the non-canon Metal Gear Solid: VR Missions and Snake Tale E: External Gazer, where having giant Kaiju versions of the game's standard Mooks is kind of a recurring in-joke. Genola is just a giant Genome soldier in white Arctic camouflage, and Gurlugon is a Gurlukovich soldier with fins along its spine and the ability to shoot paralysing Eye Beams. The one narrative game mode featuring them never mentions their guard-like appearance at all and has Gurlugon simply regarded as a sea monster, possibly referencing Special Effects Failure (however, when battling Gurlugon he has similar weaknesses to the in-game guards, like a fondness for pornography, and he will carry Raiden off Fay Wray-style if you have him put on a Gurlukovich uniform).
Disgaea: FLONNEZILLA! Flonne's final attackas a fallen angel. She dresses up in a patchy dinosaur costume and starts terrorizing the targets, with toy planes on wires flying around her. She finishes it up by breathing fire on the target.
Daikaiju no Gyakushu ("The Giant Monster Strikes Back"), a 1986 Arcade Game by Taito.
Bowser, in many of the later games, has the ability to turn into Giant Bowser/Giga Bowser, becoming a full-stop kaiju. In this case, he resembles a more evil version of Gamera.
The second Ace Attorney Investigations game has Bullmoth, a giant lizard-bull hybrid that stars in an in-universe movie. In true Kaiju form, it's facing off against another big monster from the franchise, Gourdy.
Kaiju-a-Gogo, a PC game currently in development, involves players taking on the role of mad scientists who create giant monsters to dominate the planet.
The NES Godzilla Creepypasta warrants its own spot here because the creator actually came up with many all-new monstrosities, including the Big Badwhose final form easily dwarfs Godzilla, and can be estimated to be about 400-500m tall.
Worm includes a particularly formidable bunch called the Endbringers: essentially kaiju with superpowers. The first encountered in the story is called Leviathan, and while he 'only' stands a few storeys high he can summon continuous tidal waves and is nigh-invulnerable. Others include The Simurgh, who sees into the future and specializes in Mind Rape, and Behemoth who can disintegrate anything that comes within a few meters of him and can keep fighting even when reduced to just a skeleton.
Avatar: The Last Airbender has four of these: The Unagi in Kyoshi Bay (that needs water, and therefore cannot attack the village); The Serpent from the Serpent's Pass (hence the name); Koizilla, the Fan Nickname for the Aang/Ocean Spirit Cross-fusion; and the currently unnamed Vine Monster that can be created by Huu.
An early Superman Theatrical Cartoon had the Man of Steel having to deal with a dinosaur the size of an office building that had thawed out of an ice block and attacked Metropolis.
From The Tick comes Dinosaur Neil, a man in a dinosaur suit turned gigantic humanoid dinosaur.
Trypticon, the city-form Decepticon from the original Transformers cartoon, resembles Godzilla in his robot mode, and is an obvious homage to classic kaiju films. Even more so in Transformers: War for Cybertron, he's taken the Godzilla homage Up to Eleven, with some Mechagodzilla added in to boot. And not forgetting the titanic Decepticon City Transformer, Scorponok.
Dexter's Laboratory features several kaiju. More memorable ones involve an extra-dimensional horror with many eyes and tentacles (the start of a Stable Time Loop) and iconic Dexter "oops". Another episode involved Dexter and Dee Dee becoming giant monsters by drinking Dexter's monster potions and having an all out battle (complete with Calling Your Attacks). Finally, there's Badaxtra, the monster of the original Finale who nearly destroyed the world.
An episode of Duck Dodgers parodying anime and other Japanese tropes had a kaiju called Maninsuit.
The Inhumanoids premiere episode had Tendril shambling through San Francisco, trashing streets and tossing cars at helicopters.
Star Wars: The Clone Wars features the Zillo Beast, which is a Kaiju for the Star Wars Universe, though its plot is similar to that of King Kong...initially...
My Little Pony: Friendship Is Magic had a rampaging blue bear that was covered in stars and was as large as your average house even when it's on all fours. This is the Ursa Major's baby, the Ursa Minor. The actual Ursa Major makes that one look absolutely puny.
The Season 2 episode: "Secrets of My Excess" has Spike (a baby dragon) transform into a giant angry dragon that rampages through Ponyville. And as revealed in "Cutie Mark Chronicles", a filly Twilight Sparkle exposed to the Sonic Rainboom had a Wild Magic moment that briefly turned Spike into a massive dragon.
In one episode of What's New, Scooby-Doo? set in Hong Kong, the Monster of the Week is a robot designed to look like Shaggy which is turning into a kaiju. And at one point the real Shaggy is put in a rubber suit in a model city to convince him.
As the family is leaving Tokyo, the plane warning lights for Godzilla holding the plane light up.
Captain: Uh, folks, we're experiencing some moderate Godzilla-related turbulence at this time, so I'm going to go ahead and ask you to put your seatbelts back on. When we get to 35 thousand feet, he usually does let go, so from there on out, all we have to worry about is Mothra, and, uh, we do have reports he's tied up with Gamera and Rodan at the present time. Thank you very much.
A hobo tells the story of Paul Bunyan where he pushes Rodan, who then falls over Babe the ox. Lisa informs him that never happened.
In the first segment of the Futurama, episode "Anthology of Interest I", Prof. Farnswoth turns Dr. Zoidberg into a kaiju so he can fight a 500 ft. Bender, with predictable results.
Quite a few dinosaurs fit this trope. In particular Amphicoelias was by some estimates the single largest land-based animal — never mind dinosaur — on record. 40 to 60 metres (130 to 200 ft) in length, and may have had a mass of up to 122 metric tons (135 short tons).
At half a meter long, Anomalocaris wouldn't qualify as a kaiju today, but considering it lived in an era when the largest non-Anomalocaris animals tended to be measured in a few inches, it certainly was at the time.
Anteaters, aardvarks, and pangolins are this trope for termite "cities".