I didn't really have "that one game". I rented most games on NES and SNES. NES I'd have to say Super Mario Bros 3, and probably Rock N Roll Racing on SNES.
N64, I'd have to go with Goldeneye 007 - although Zelda: OoT and MM are both very close to it. OoT definitely reminds me of Christmas, though. The game was released in November or something, and I preordered it with my mom but she was giving it to me for a Christmas gift so I had to wait. This was a game I've been reading about incessantly in Nintendo Power and let me just say that Christmas Eve I got about 1 hour of sleep.
It was extra special because not only did I get the gold case, my mom was one of the first people to pick it up so I got a Zelda t-shirt too!