In DKC3, when you enter Wrinkly's Save Cave, on occasion Wrinkly will be playing her Nintendo 64, as evidenced by the music being an Expy of the Super Mario 64 "Inside the Castle Walls" theme note note they are not the same pieces of music: compare the original theme here and the DKC3 version here.
Also in Wrinkly's Cave, sometimes she will be sleeping, and the background music will be the baseline from the "Jungle Hijinx" tune from the first game.
Bad Export for You: "Jungle Fantasy", the Japanese OST for the original DKC, contained seven arranged songs, all exclusive to the soundtrack. The OST was eventually released in Amercia as "DK Jamz", though out of all the arrangements, it only contained Jungle Groove, leaving out the other six songs (twoexamples).
Follow the Leader: It was obviously based on Super Mario World, but it does have its own original elements, like a frontal rolling attack, minecart rides, and secrets hidden in the walls. Though some still slam it for being a Mario clone.
Keep Circulating the Tapes: The original DKC trilogy was removed from the NA and PAL Wii Virtual Console services for reasons known only to Nintendo, meaning the only way to get copies of the game is finding either the original SNES cartridges or the GBA remakes. That is until October 2014, where all three SNES games were released for the Wii U's Virtual Console (along with the Donkey Kong Land games for 3DS) in Europe and February 2015 for America.
However, the Wii Shop Channel versions are set to become this once again. Due to the impending shutdown of the Wii Shop Channel itself, this won't be reversed barring any unforseen circumstances. You won't be able to add Wii points to the service in early 2018, and the channel is set to shut down entirely in 2019, meaning even redownloading already purchased games will no longer be an option. Welcome to the digital age, where circulating the tapes isn't even an option anymore.
Killer App: The original ended up being the deciding factor in the SNES defeating the Genesis in western countries. DKC actually ended up becoming the top selling video game that gen that wasn't bundled.
Market-Based Title: In Japan, the SNES trilogy was known as Super Donkey Kong. The Retro Games, no longer on the SNES, simply dropped the Country from their names and were called Donkey Kong Returns and Donkey Kong Tropical Freeze.
Cranky was meant to be a lot nicer during development of the first game, as seen here. According to early concept art, Cranky was originally named "Grandpa Kong" and looked like a white version of Donkey Kong with a beard. This may have influenced his characterization in some of the spinoffs such as DK: King of Swing, which made him nicer than he typically is.
A giraffe animal buddy was planned for the first game, allowing DK to climb the giraffe's neck to reach high areas.
DKC2 has some sprites of Diddy and Dixie mourning, which have been Dummied Out. They seem to have been meant for when they lose a bonus game much like with DK and Diddy in the first game, rather than the screen freezing in the actual game.
Concept art shows that K.Rool originally was named "Krudd".
The Kremlings originally had a more Battletoads-esque design and were blue.
The earliest known plot involved the Kremlings stealing a "Golden Banana", causing Donkey Kong and Jr to have to get it back. The Golden Banana made it into material such as the cartoon.
An unused plot for the first game was a crossover with Wario named Donkey Kong Vs Super Wario.
The fan favorite BGM Stickerbush Symphony almost didn't make it into DKC2. It was originally designed to be for underwater levels, but these didn't end up in the game (the closest would be levels that take place inside flooded pirate ships). Instead, the soundtrack was used for the bramble levels to juxtapose the difficulty of them.
Fan Nickname: DK Vine members like to call the show Lord Harry. The person who coined it did so initially to distance it from the games, feeling it was a bad show, though the members who like the show, or at least warmed up to it, started using it as an Affectionate Nickname more than anything.
Keep Circulating the Tapes: Outside a handful of episodes released on VHS and DVD, a complete series has yet to surface in any English speaking countries.
Non-Singing Voice: Used in the English version with Donkey Kongnote and only Donkey Kong, everyone else, for better or worse, keep the same voice actors for the show's song numbers. Otherwise averted in the foreign releases.
The Other Darrin: King K. Rool was voiced by Len Carlson in the pilot episode "Bad Hair Day", and then by Benedict Campbell for the rest of the show's run.
What Could Have Been: According to writer Erika Strobel, the reason for Nelvana's collaboration with MediaLab was because the latter fired the original writers for coming up with scripts that were racist, sexist, and inappropriate for a children's show. Since they already storyboarded 10 of those episodes, Nelvana had to write around them.
The unaired pilot episode (which is an alternate version of the episode "Bad Hair Day") had different voice actors for almost all the characters including Donkey Kong as you can see in this MediaLad promotional tech demo for the show.