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).
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.
Killer App: The original ended up being the deciding factor in the SNES defeating the Genesis in the West. DKC actually ended up becoming the top selling video game that gen that wasn't bundled.
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.
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 Stickerbrush 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.