First thing I thought of was
Super Mario World for the SNES. You can take turns as Mario and Luigi clearing the areas co-op style. And definitely one of the absolute best Mario platforms ever made (I downloaded it from the Virtual Console for my Wii!)
Banjo-Kazooie and
Banjo-Tooie for the N64 was always fun for the wife and I. Kept us busy for hours at a time. One of the better 3D platformers by
Rare. Take turns clearing levels or swap when you die.
For real co-op platform gaming, I always liked
Contra III: The Alien Wars for the SNES. Side scrolling and several top-down levels made for fun gameplay.
As you can tell, I'm a classic Nintendo fan. Enjoy!