Another vote here for the N64 version. Damn, I had some good times playing that in my early teen years, by myself and with my friends. I'll echo the sentiment that it was an excellent multi-player game, and it remains a fond memory of my childhood amongst some not-so-fond ones. Like canadaboy_32, my friends and I would always fight over who got to play as Yoshi -- with me usually winning by virtue of it being my game and my system. 
One of my favourite cheats was jumping from a high point in the track to a low part on the other side in Rainbow Road. I managed to pull it off a few times, but man was it tricky.
The only other version I played was the Super NES game, and it didn't really do as much for me. Maybe it was because I didn't own that one, and thus never really got the chance to practice and get too skilled at it.
This is really making me want to dig out my N64 and play some Mario Kart. If only I had somewhere I could hook it up...

One of my favourite cheats was jumping from a high point in the track to a low part on the other side in Rainbow Road. I managed to pull it off a few times, but man was it tricky.
The only other version I played was the Super NES game, and it didn't really do as much for me. Maybe it was because I didn't own that one, and thus never really got the chance to practice and get too skilled at it.
This is really making me want to dig out my N64 and play some Mario Kart. If only I had somewhere I could hook it up...