Corporal, I'll try to explain what I like about the Rare DK game (with the caveat that I only like, nay love, the first two, and abhor DKC3).
spoiler (click to show/hide)
long carepost incoming
The first game came out when I was 12, and at the time there was nothing like it graphically. Nowadays pre-rendered graphics are seen as nothing more than a cheap gimmick, but back then it was unheard of. It made a huge impression on that front alone. The game was Nintendo's effort to revitilize the SNES platform, as I believe the PSX had come out by that time. And DKC, although restricted to the 2D plane, looked a hell of a lot more polished and detailed than the early PS 3D games.
Now, graphics are important, but superficial. What kept me playing is the art style, the music, and the game mechanics. There's something that Rare got so perfect about the mechanics and physics of the game that I still find lacking in the Retro sequels. It just feels right, it feels great to bounce and roll around as Donkey or Diddy. When I first fired it up, you can go into Donkey's little treehouse in the first level. It's a simple little sandbox where all you can do is bounce around on a tire. But it feels
so satisfying . And that little segment right there is the selling pitch for the entire game.
The game play can be described as kinetic. The physics/mechanics are set up that you can simply hold down the d-pad to run forwards and if you see a chain of enemies bounce off each one with perfect precision without stopping and without much effort. In many respects, it's more fast paced than Sonic games wish they could be. Yeah, Sonic gets super fast, but you have to stop all the time. You can run through most DKC levels without stopping. And it feels amazing.
Also, while it's not the most complex platformer, it did introduce a lot of cool mechanics that were unique to it (afaik). Blast barrels, bouncy tires, hooks suspended in the air, mine cart levels, levels where you spend the entire level on a moving platform that you have to refuel so it doesn't fall down. Animal buddies. Water levels where the water becomes boiling hot so you have to basically hit switches so you don't die.
The games' art design and sound design was also dripping with personality, which made me fell in love with it as a kid. I know a lot of people dislike the ubiquitous Rare design of googley-eyed mascots, but I think the first two DKC games were the pinnacle of Rare's design without becoming too goofy or cutesy. Hell, the fact that they've kept the same Donkey model that Rare created after all these years is testament to the timeless design. The enemies are all varied and have their own personality. You have the fat man-boobed Klumps, the muscle-bound Krusha's and Crunchya's, the tiny ankle biters Klampons and Klaptraps, etc. And they all make a satisfyingly hilarious croaking sound when you jump on them.
The level backgrounds are also beautiful and varied with many layers of paralax scrolling: whether it is rows of palm trees, silhouetted by the setting tropical sun, or imposing spruces, or treetop houses reminiscent of the Ewok village in ROTJ, pirate galleys, industrial backdrops of factories, snowy landscapes, I could go on and on.
And I won't even waste time singing praises to David Wise's masterful compositions. He is well regarded.
Fuck it, I am getting too verbose in trying to write a love letter to my favorite games, just watch these two videos: VIDEO VIDEO 
