While Mario Kart has been king of kart racing games since 1992, it has seen many imitators and rivals. Diddy Kong Racing was the first kart racer (that I know of) that Nintendo had done outside the Mario series. Though technically Rare (who made the Donkey Kong Country series) were the real team behind it.
It featured a similar set-up to Mario Kart, with racing through colorful themed tracks with power-ups to use. The cast didn't feature Diddy Kong's famous uncle, but original characters. Most notable would be Banjo the bear (who would later star in Banjo-Kazooie) and Conker (the star of Conker's Bad Fur Day) the squirrel.
What also set it apart from Mario's was the ability to use hovercraft and planes. The game received a very positive reaction from critics and gamers alike. It's often remarked as one of the most beloved N64 games, with many thinking it was superior to Mario Kart 64.
No real sequel was ever released as Rare left Nintendo for Microsoft. Though surprisingly they came back to develop a remake of Diddy Kong Racing for the Nintendo DS. It featured online-play, but Conker and Banjo were absent. Though ironically despite some improvements, the DS remake received a mixed reaction. It wasn't considered terrible but it was vastly overshadowed by Mario Kart DS.