This was actually the format for Sonic X, with Sonic and his Furry pals as the "monsters" (albeit cute ones) and the Thorndyke family as their human allies. This was ostensibly to give the audience a human identification character — Chris. They quickly dropped The Masquerade though, and Sonic became an instant celebrity.
Implied with the theme song for Samurai Pizza Cats, although the actual show doesn't follow any of the trope's characteristics.
Going way, way back, the original X-Men basically started off this way, minus the pet human.
Conversational Troping in an early-90s issue of Green Lantern set at a toy expo: "Buddy, every ten minutes I've got someone trying to sell me 'the new Turtles'. I've a warehouse full of stupid dinosaurs named after dead presidents!"
Many other anthropomorphicanimal superhero comics which were "inspired" by the Turtles. They spawned a bunch of "adjective, adjective, adjective, noun" anthropomorphic imitations/parodies, but those were mostly dreamed up by fans and wannabe pros looking to cash in (TMNT #1 was VERY rare and up to $2-300 in demand). This didn't stop until it crashed the comic market (the famous "black and white implosion" which was a dry run for the Dork Age market collapse).
Averted with Samurai Squirrel, a two-issue fling that was serious and more story-driven
Mini-Comics Included is a series of mini-comics based on toylines that aren't real but could easily have been; Prime-8s, about a squad of 8 intelligent, superpowered apes and monkeys, is partially based on TMNT and this trope in general. This group was a little larger than most, and had two females.
Often parodied on Late Night With Conan O'Brien, where Conan's mock fall previews often feature programs such as Embryonic Rockabilly Polka-Dotted Fighter Pilots or Country Cuckoo-Clock Codpiece Zulu Warriors.
The live-action show Dark Angel was similar in premise, with the exception that most of the Chimera could at least pass for human (with the notable exception of Joshua in season 2). Nevertheless, Logan acted as a Secret Keeper for Max and the rest.
In-show commercials in the first episode of Round House gave us these parody titles: "Adolescent Deformed Tai-Kwon-Do Tortoises", "Pre-teen Genetically-altered Martial Arts Iguanas", and "Kinda Young Really Screwed Up Karate Koalas".
In the wake of the craze, Ray Stevens recorded "Teenage Mutant Kung Fu Chickens", about a quartet of fighting chickens.
Although the Autobots never really hid from anyone in the original series. They were acknowledged by the world's leaders as early as the end of the three-part pilot.
In the TV show, that is. In the comic, the world remained fearful of all Transformers, regardless of faction. The Autobots had a few reliable human allies like Buster Witwicky and G.B. Blackrock, but they were few and far between.
Gargoyles — with Elisa Maza as their human ally. Gargoyles was one of the few shows to acknowledge that a situation like this simply can't last forever, and slowly had the Gargoyles transition from complete secret, to urban myth, to publicly known... and feared.
Street Sharks — with a Surfer Dude as their human ally. (The Sharks themselves used to be human surfers as well... it's complicated.)
The Mighty Ducks cartoon, which may as well been called "Hockey-Playing Twentysomething Extraterrestrial Mallards". About a group of anthropomorphic ducks from a world surronded by puck-shaped asteroids where hockey is Serious Business (...you mean they're Canadian? *rimshot*) fighting space dragons and posing as a regular hockey team in modern-day California. No, really.
To be fair, they 'pose' as a hockey team by actually playing hockey in a league. But they still fight space dragons and villains-of-the-week. They're pretty much outed as aliens in the first few episodes.
The Darkstalkers cartoon, with Felicia, Jon Talbain, Sasquatch, Rikuo, and later Hsien-Ko as the good guys, with a wizard named Harry and a butler named Klaus as human allies. Pyron, Demitri, Raptor, Anakaris, and even Morrigan were bad guys, and Bishamon, Donovan, and Hutzil showed up as neutrals.
The 1993 series Stone Protectors attempted to market the troll doll craze to grade school boys. The heroes are an awfulFake Band from New York City who are transformed into troll-like super heroes by magical crystals, then have to protect the crystals from the Saurians, reptilian bad guys who would use their powers for evil. The problem of hiding the conflict from the public is averted because the heroes are quickly transported to the Magical Land where the crystals came from.
There were also Trollz, produced about 10 years later, which did the same thing, but for a female audience (read: It ripped off Winx Club and Sailor Moon instead of the TMNT.)
Kung Fu Dino Posse, a 40-episode cartoon series that aired on Starz in 2009, is an homage to several Secret Mutant Hero Teams before it, including the Street Sharks spinoff Extreme Dinosaurs and TMNT. In modern times, a quirky science geek accidentally thaws out four anthropomorphic dinosaurs, whereupon they inflict inexplicable Kung Fu upon evil raptor villains and their army of generic mutants. The series is well aware of its own cliches and often leverages them for comic effect.
Bucky O'Hare was this In Space, with the strange twist that the anthropomorphic animals are the norm, and it's the human character that has to be kept hidden from that reality's "muggles".
Parodied in The Fairly Oddparents movie "Channel Chasers", where one of the TV shows Timmy travels through is "Adolescent Genetically-Altered Karate Cows".