Any console, it just has be a game where 3 or more players can play at once, offline.

For me, the N64 is the undisputed king for these type of games. I probably dont even have to mention them but 007, Mario Kart, Mario Party, and Smash Bros.

Outside of that, I liked Halo, Fuzion Frenzy 1 and Gauntlet Dark Legacy. I was never able to play 3+ multiplayer on Hunter the Reckoning but thats one of my favorites. Crash Team Racing was fun as well back in the day.