While Donkey Kong is part of the Super Mario series, there are Easter Eggs that also appeared in other series created/licensed by Nintendo.
In Banjo-Kazooie, Funky Kong and one other character were mentioned in Gruntilda’s Furnace Fun as incorrect answers, causing Banjo and Kazooie to lose one unit of energy (or fall into the lava and lose a life if they failed to answer the question on a Skull Panel). An obnoxious gorilla sound was used by Donkey Kong in Mario Kart 64, Mario Party 64 games, Mario Tennis, and Mario Golf.
In Banjo-Tooie, Donkey Kong appears as an Easter Egg, but in the form of a doll carried by one of Bottles’ children while Banjo and Kazooie are on a quest in the Isle of Hags to resurrect Bottles and defeat Gruntilda once more.
Diddy Kong can be used as an outfit by Mario in Super Mario Odyssey under a couple of circumstances. Donkey Kong also appears in an 8-bit enemy while Mario participates in one of the main events in New Donk City, where Mayor Pauline sings the “Jump Up Super Star” for the Multi-Power Moon. Even some names in the Donkey Kong Country series, including K. Rool’s name, were used in certain places as Easter Eggs.
In the Donkey Kong Country SNES game, the girders were used as a sort of table, where Cranky Kong is just playing the retro Donkey Kong arcade music on the phonograph. This is an Easter Egg: when Donkey Kong comes down from above to take over the music intro theme and turn it into a rockabilly theme in the Jungle.
In Donkey Kong Country: Tropical Freeze, the classic Donkey Kong Country intro music plays on the phonograph in one of the levels where you ground-pound near the phonograph. Also, the television show titles of Donkey Kong Country Returns when Donkey Kong ground pounds the inside of the ruined plane in the first level of World 1.
Donkey Kong and Donkey Kong Jr. appear in the arcade games Punch-Out! and Super Punch-Out! alongside Mario and Luigi on both sides, where you manage to knock down every last opponent as the Challenger, whose name is revealed when you start playing. In the Wii version of Punch Out!, the black form of Donkey Kong also appears in the background when you stun Mr. Sandman and do not attack him for a bit. Donkey Kong also appears as a secret boss during Mac’s Last Stand, with intermissions and challenges in the Exhibition as well.
In The Super Mario Bros. Movie, created by Universal Studios and Illumination, Donkey Kong appeared as a main character alongside Cranky Kong, while Diddy Kong, Dixie, Chunky, Kiddy, Swanky, and Funky appeared as Easter Egg characters. The DK Rap was also played shortly after Donkey Kong made his entrance into the Arena held in the Jungle Kingdom before fighting Mario. The Rocket Barrel scenario was also shown to help Donkey Kong and Mario escape being eaten by Unagi and save Luigi, Peach, Toad, and the Mushroom Kingdom from falling to Bowser.
In The Super Mario Galaxy Movie, also created by Universal Studios and Illumination, Donkey Kong also appeared as an Easter Egg in New York City during Yoshi’s scenario in New York City before he fled to the Mushroom Kingdom to escape a criminal fate. The Hammer prototype and Hammer gimmick from the original Donkey Kong arcade game were played humorously by the Minions from Despicable Me during the Illumination intro title screen.