Animal Crossing Plaza bears an extreme resemblance to the WaraWara Plaza, and in fact was explicitly described as the Animal Crossing equivalent.
Fortune Cookie prizes in New Leaf are all from other Nintendo games or even Nintendo products, but as an extra, when you equip a clothing item or touch some of the furniture, they play the appropriate sound effect.
In City Folk, Kapp'n's trophy from Super Smash Bros. Brawl can be seen near Kapp'n himself while riding on the bus.
Goldie's picture quote in Wild World onwards is "I'm really into that Lab on the cover of Nintendogs. He's pretty dreamy." To be specific, she's referring to the labrador retriever on the box art of Nintendogs: Labrador & Friends.
The Creepy Clock furniture item is almost identical to the "13-hour clock" from The Haunted Mansion.
A rabbit named Snake wears a Ninja costume. Ninjas are known for their stealth.
All items in the Mario Theme sell for 256 bells, a reference to the Nintendo Entertainment System's 256 bytes of OAM, as well as the maximum amount of variables usable in an 8-bit binary (the NES' 6502 processor is 8-bit).
The way cockroaches die is very similar to the way Pikmin die in that their spirits float up into the sky.
"Rockin' K.K." is incredibly similar to the "New Age Retro Hippie" music from EarthBound, especially the intro (which in turn was based on the opening of "Johnny B. Goode" by Chuck Berry).
The "NTDO Shirt" is a shirt with the text "NTDO 1889", 1889 being the year Nintendo was founded.
K.K. Slider is intended to be a reference to sound designer Kazumi Totaka, hence his proper name being "Totakeke", although his singing name is likely a reference to "C.C. Rider" by Chuck Willis, and could be a reference to K. K. Downing, a real-life guitarist.
Phil is an ostrich, but looks more like Falco Lombardi than any real-life ostrich. Likewise, Louie looks like Donkey Kong, though his name and clothes are a reference to Luigi.
Frank the eagle (who was introduced in Animal Forest e+, but absent in the games released between then and New Leaf) is called Hulk in the Japanese version of the game, is green, and his initial phrase is "crushy."
Octavian's design request in Happy Home Academy is a "squid showdown citadel." This request unlocks, among other things, a paint-splatter pattern for house exteriors, squid and octopus-themed chairs, and a samurai helmet (referencing Splatoon's final boss).
A more or less Dub-Induced Plot Hole avoids showing that the villager a bear called Klaus in the English versions looks sorta like Gaius Julius Caesar; this is shown even better in Happy Home Designer where he wants a Roman bath.