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 some other character were mentioned in Gruntilda’s Furnace Fun as as incorrect answers causing Banjo and Kazooie to lose one unit of energy (or fall into the lava and lose a life if 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 a Easter Egg, but in a form of a doll carried by one of Bottle’s 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 used by Mario in Super Mario Odyssey under couple of circumstances. Donkey Kong also appears in an 8-bit enemy while Mario participates in one the main events in New Donk City where Mayor Pauline sings the “Jump Up Super Star” for the Multi-Power Moon. Even the some names in Donkey Kong Country series, including K. Rool’s name, were used in certain places as Easter Eggs.
In Donkey Kong Country SNES game, the girders were used as some sort of table where Cranky Kong is just playing on the Phonograph player the retro Donkey Kong arcade music piece. This is an Easter Egg when Donkey Kong came down from above to take over the music intro theme and turn it into a rockability theme in a the Jungle.
In Donkey Kong Country: Tropical Freeze, the classic Donkey Kong Country intro music pieces is heard in the phono graph in one of the levels where you have Donkey Kong ground 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 who must named 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 knock 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.