Finally some other old-school gamer on this forum!
I love all their games, but Donkey Kong Country 2 captivated me the most. The environments and graphics were so nice laid out I was completely sucked into it. I never collected enough coins to unlock the Lost World though.
Another awesome aspect of that game is the music. The original DKC had awesome music, but in DKC2 it was divine!
As an AS diagnosed musician, I pay more attention to music than other aspects in multimedia.
Needless to say, all their titles were revolutionary for its time. What I liked about Killer Instinct was the fact that it was a fusion of Mortal Kombat and Street Fighter. The characters were awesome and varied. Glacius and Fulgore were my favourites.
Killer Instinct Gold(for the N64) was a major downstep for Rare, as were all of their titles for the N64.
What made them awesome was their use of ACG(Advanced Computer Graphics). The graphics were rendered as three dimensional models and "photographed" digitally to make sprite(2D) images out of it.
I like that feel more than the true 3D that they built upon in their newer games because Nintendo-3D looks like Toy Story.
I liked the real DK better than the plastic one

My favorite game is Donkey Kong country 2 as well the music really captures the imagination! as with the graphics and the gameplay! The Music from the bramble levels
pushes the SNES sound chip to it's limits donkey kong 1 was good I didn't think much of donkey kong country 3 though.