The Animaniacs short "The Warners and the Beanstalk" (which parodies both Jack and the Beanstalk and Green Eggs and Ham) had a series of scenes where the Warner siblings were trying to get the giant, who looks and sounds like Ralph the Guard, to try gold eggs and meat. One "verse" of the sequence has a scene-shift to modern-day Tokyo, with them quipping, "Would you eat them in Japan? With Godzilla and Rodan?" (And unfortunately for Ralph, both monsters are right next to him, and clearly don't like him too much.)
Joey and AP have fought a bunch of giant monsters in Atomic Puppet like a giant mutant spider, a fire-breathing hydra-turtle, a giant robot with magnet powers, and a giant mucus-spewing slug.
Avatar: The Last Airbender has four of these: The Unagi in Kyoshi Bay (that needs water, and therefore cannot attack the nearby village); The Serpent from the Serpent's Pass (hence the name); the Aang/Ocean Spirit Cross-fusion; and the currently unnamed Vine Monster that can be created by Huu.
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.
King Kong appears in "The Ducky Horror Picture Show", a Monster Mash episode of DuckTales (1987), and climbs Scrooge's tower.
In the first segment of the Futurama, episode "Anthology of Interest I", Prof. Farnsworth turns Dr. Zoidberg into a kaiju so he can fight a 500 ft. Bender, with predictable results.
Spoofed in The Grim Adventures of Billy & Mandy episode "Giant Billy and Mandy All-out Attack" (a reference to the Godzilla movie Godzilla, Mothra, King Ghidorah: Giant Monsters All-Out Attack!) where Grim takes Billy and Irwin to see real kaiju. They meet Kragera, (a Gamera parody) and Kittygra (a cat version of King Ghidorah). Billy also turns into a spoof of Ultraman while Mandy pilots a giant gorilla robot called Mecha-Gorillasaur (a parody of Mechani-Kong and Humongous Mecha). Grim also mentions in the episode that most giant monsters aren't giant any more due to eating healthier diets.
The Great Grape Ape features a friendly Kaiju, in the form of a 50-foot purple ape.
The Inhumanoids premiere episode had Tendril shambling through San Francisco, trashing streets and tossing cars at helicopters.
The numerous giant-sized monsters in The Last Kids on Earth which came to earth through portals from another dimension.
In The Legend of Korra, one appears in season two. When Korra's uncle Unalaq fuses with Vaatu, the embodiment of chaos and darkness, after destroying the embodiment of light and peace, they transform into a gigantic red/purple/black monster that looks like a fusion between the two fusees. It can create Spirit Wilds, use the currently-omnipresent Aurora Borealis to teleport and fire a destructive chest beam.
Let's Go Luna!: The educational focus of the episode "Lizardzilla!" is the kaiju genre of movies that are popular in Japan.
Men in Black: The Series has an episode that shows a giant Fmek and one of the Worms fighting Kaiju-style in the city. The joke is that they are two of the smallest alien species and were increase in size by Applied Phlebotinum.
Metalocalypse has Mustakrakish, the giant Finnish lake troll. No, not THAT kind of giant troll.
My Life as a Teenage Robot: Jenny (the title robot) encountered a few during the show's runtime. The most notable were probably Armagedroid, an immense robot with the sole purpose of destroying weapons but had gone crapshoot in peacetime, and Gigawatt, an extraterrestrial being that fed upon energy (though he didn't start out kaiju-sized, the consumption of New York's electricity did).
There's a rampant blue bear that is covered in stars and is 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.
Ninjago: In the Season 5 finale, the Preeminent (leader of the Cursed Realm) is revealed to be a rampaging Genius Loci kaiju that yearns to curse the rest of the Sixteen Realms.
Also The Great Devourer. Pretty much just the Ninjago version of Jormugandr from norse mytholgy.
The Powerpuff Girls frequently fight Kaiju assaulting their City of Adventure when not engaging their Rogues Gallery. One is actually called a Ro Beast. Smarter than they look, they can talk, and the Girls are friends with at least one of them. They all come from a place called Monster Island, and they apparently consider it a rite of passage to stomp into Townsville and fight the Girls. Yet another way in which the city would actually be safer without them around.
Primal (2019) features a kaiju-sized horned theropod, a giant spider, a rampaging zombified-sauropod and a Megalodon as several of the enemies that Spear and fang have to deal with.
"The Revenge of Murray the Mantis": A spirit taking control of a giant mantis balloon has to be stopped by releasing the Marshmallow Man from the Containment Unit for them to fight each other.
"Cold Cash and Hot Water": A more serious approach: after Peter's father and notorious con artist steals an ancient demon from Alaska to exhibit it in New York, the demon get loose causing havoc in the city.
Schoolhouse Rock!: The titular "Tyrannosaurus Debt" from Money Rock, a massive red, white, and blue T. Rexpy that represents the United States' ever-increasing national debt. The people of Washington, DC attempt to keep it under control by feeding it with taxpayer money, but nevertheless it continues to grow in size because the US Government can't repay its debts quickly enough.
While they aren't as big as other examples, the Seven Little Monsters are pretty dang large.
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.
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...
Alexandrite, the fusion of all three of the Crystal Gems, from Steven Universe is big enough to be considered one.
In the limited series Steven Universe: Future, Steven abruptly turns into one in the ending of the episode "Everything's Fine" as a result of his breakdown. This form fully debuts in the next episode, "I am my Monster".
An early Superman Theatrical Cartoon from 1942, "The Arctic Giant", 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. Interestingly, the design of the beast, which was called a Tyrannosaurus rex in the cartoon, looks a lot like Godzilla despite the original Gojira being introduced twelve years later.
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.
In one episode of What's New, Scooby-Doo? set in Tokyo, 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.
An accident with the Miniaturizer turns Hercules, a (normal) giant Hercules beetle, into this trope temporarily on Wild Kratts.
