It has to be one of those games where random shit can happen at any time.
Super Smash bros is one of those games. Seems like every time we play something unexpected happens.
Something classic like a collection of old arcade games would be good too, or maybe some old-fashioned card games. Basically any game with a high-score to beat is a good choice, like Tetris.
Basically any RPG can be beaten once 100% and that's it, so that'll get boring. I guess you can challenge yourself to bet it in different ways or as fast as you can, but meh, seems like that would get very boring.
I guess I would choose the original super smash bros for n64. There are high scores to chase (if you keep track of them), different ways to beat the game, it's challenging, random things always happen.