Mario Kart (series)

The best way to describe this series is straight from the experts, those at the Super Mario wiki.

Quick Summary
Mario Kart is a truly inspired racing game created for the well-known characters in the Mario franchise. These games feature the heroes, the villains and a few in between to create a diverse roster of racers to pick from. Once a character is chosen, one can decide on karts, which have just as much variety. Other options may come up, then it's time to choose what cup you are going for. There is a nice number of cups each representing about four races. Do well in each, and you'll win the cup and possibly get a good rating. Do bad, and...take a guess. Beyond the Grand Prix, there are other options to choose from. There is time trial, battle and vs. Battle and Vs. mode can be played with friends, so don't forget to practice. Battle pits your wits against other racers in a chance to win or take out a number of objects. Vs. tests your skills at a number of user-selected races. Mario Kart allows online play and a few other options.

Benefits of basing your game off these ones

 * Revolving around racing, with many tracks already being retro, the additional tracks shouldn't be too hard to imagine.
 * Add new battle modes with new tracks, and an over-all new gimmick, and you're set!
 * Not too many changes each sequel

Limitations to keep your game believable

 * Reasonably well-known Mario characters only, no exceptions (except for the game that had Pac-man and ghosts).
 * Not too many changes each sequel
 * Mario, Luigi, Toad, Bowser, Peach and Yoshi must be present to keep tradition alive.

This article describes Mario Kart. Some may decide they like the racing, and make a new series without Mario. And that means it is no longer Mario Kart, so they can do whatever they want.