I'd take my Sega Saturn with Worms and Super Puzzle Fighter II Turbo. These are based on the premise of replayability. There are plenty of great, in-depth games on each system but these are two I usually pull out for events or gatherings. For me I can only relive a story line and explore a static world but so many times, leaving many sports, adventure, and role playing games out of thought.

Worms has been a great series for replay value with the customizations available in each custom game. This game entertains for hours and quite competitive with others.

Puzzle Fighter falls under similar qualities where one can run through various difficulties of the game to take on Akuma or take turns burying each other with gems. I've always enjoyed the art and music in this game.

If we were permitted to import then I would swap Super Puzzle Fighter II Turbo with Magical Drop III. It's a tough and fun game in story mode and the versus offers challenging, nail biting replays.