Oh boy. Despite the show clearly being an American live-action sitcom, there are lots and lots of people on the Internet who make various memes and comments that refer to the show as an "anime".
"What the fuck happened to real anime? What happened to real good story and characters?"
"Perfect animes don't exis—" (picture of Cory in the House poster ad)
A video called "TOP 27 ANIME BOOBS" once circulated YouTube, and it was really parts of the intro to the show synced to Crashman's theme from Mega Man 2 (followed by the same thing with Hill Top Zone from Sonic the Hedgehog 2 and Phil of the Future), which is probably how the memes and comments of the show being an anime started in the first place. A remastered version minus the Phil of the Future segment can be found here.
The handheld licensed game has become a meme on the /vp/ board of 4chan. Whenever there's a game being leaked there's a high chance you'll get that game instead. The game is also commonly called one of the greatest games ever made, to the point where it has a Metacritic user score of 9.5, which is possibly the highest user-rated game on the site. Not even The Legend of Zelda: Ocarina of Time, the highest critic-rated game, got a user score that high.
The climax of "Uninvited Pest" was uploaded to YouTube under the name "The Greatest Scene in Television History", and from there it's managed over half a million views and is highly quotable.
The show's IMDb user review page. Nearly all of the reviews are 10 stars talking about what a great anime it is.
The show's title itself has become something of a Mad Libs style meme. "X in the house" generally becomes a meme whenever an election, especially an American one, takes place. The meme usually has the victor or someone memetic replace Cory in the title card on their way to the White House to become President.
"Cory in the Big House", following Kyle Massey's conviction for pedophilia.
