I never owned a Super Nintendo growing up, so I never got to play Super Mario World or A Link to the Past until much, much later in life. But even I got to try Donkey Kong Country. Is was just that huge. Everybody who was anybody had it (meaning that I wasn't anybody). Not only is this a terrific platformer, but the graphics were way ahead of their time. If you look at the sequel that just came out for the Wii, the difference in graphics isn't even that big of a leap.
Despite the mega-funness of DKC, what I'll always remember the most about it is that weird animated series spin-off that used to air on Teletoon back in the late 90s. Somehow, they managed to make the animation look just like the graphics. It was one of those cartoons that was frustrating to watch, especially since every once in a while the Kongs would break out into song with little or no warning. Cartoons are weird like that.