Mariokart Wii definitely gets the addicting award. Holy crap, I played that for so many hours. Whenever my friends and I played, I had to try to remember to 'forget' a lot of my tricks so as to not be a complete jerk while playing, lol. I think I placed pretty highly in one of the competition thingymajiggs - I can't remember which one, though. It was probably a year or more ago by now.
Mariokart 64 takes the classic award, though. That game was awesome. It was also addicting, though it didn't have much re-playability when you finished. It's still fun to play with friends once in a while, though.