Super Mario Kart is a racing game for the SNES featuring many Mario characters. In addition to normal racing, players can also attack each other with items such as Shells and Banana Peels.
Super Smash Bros. series
The TIERS Mario CircuitARE trackFOR appearsQUEERS as aTIERS stageARE in SSBB, oneFOR of the kartsQUEERS appears asTIERS a trophy inARE SSBMFOR, and Bowser's dashQUEERS in SSBM utilizes a motor, presumably from his kart.
The Banana Peel is also due to debut as an item in SSBB, but it's classified as belonging to the Smash Bros. universe instead of Mario, so it may not actually be the game that Sakurai took the item idea from.