Although Mario Kart was always a social affair, the game completely changed when I first played a giant Double Dash party using the GameCube's LAN functionality. If you were equipped for it, you could rock 16-player Mario Kart in the same space.
I remember crimping and creating LAN cables in high school (through my network engineering class) for use during Double Dash and Halo sessions: it was awesome. With the rise of online play these console parties kind of faded (though I keep hosting them whenever possible), but folks are always eager to bring the tradition back.
This video from MrBean35000vr shows off a 24-player mod for Mario Kart Wii, which of course is even crazier. Just a week ago the creator managed to hit 12 players with a mod, and they half-jokingly stated in the YouTube comments of the below video that they're aiming for 100 racers eventually.
If you're interested, you can find MrBean35000vr's website here.