PC Sidescrollers like Donkey Kong Country

Giana Sisters.

There aren't that many platformers on PC that don't also involve shooting.

While I wouldn't exactly compare it to DKC the latest Rayman game is on PC now and it has some of the same speed and flow to at least some of the levels.

Gizmos and Gadgets.

If you want a Platformer with rythm take a look at Bit.Trip Saga.
TBH there aren't many "shoot&jump" platfomers that don't imply puzzling (Braid, VVVVV, Limbo, etc) or shooting (Hell Yeah, and many more) actions :S

Rayman Origins/ Rayman Legends

It's not really the target market of PC games. At the same time the SNES was huge, FPS's had just been given a new wind and platformers were old hat.