From the Super Mario Wiki
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Excitebike is a character from the NES game of the same name. In Excitebike, multiple Excitebikers compete on course for the fastest time. Performing and landing jumps gives the characters a burst of speed. Overheating the engine or failing to land a jump will cause the player to fall off of their bike for a few seconds, losing both speed and time.
Excitebike first appears as a trophy in Super Smash Bros. Melee. In Super Smash Bros. Brawl, Excitebikes appear as an Assist Trophy. When summoned, multiple Excitebikers drive into opponents, dealing damage to them and potentially dragging them off the stage. Even though Excitebike does not reappear as an Assist Trophy in Super Smash Bros. for Nintendo 3DS / Wii U, it has a trophy in both versions, as well as a Sticker in Super Smash Bros. Brawl.
An Excitebike themed race track called Excitebike Arena appears in the Mario Kart 8 DLC Pack The Legend of Zelda × Mario Kart 8. The sprite for an Excitebiker is featured in the banner above the goal line.
An update to Super Mario Maker added an Excitebiker as one of the costumes Mario can receive upon touching a Mystery Mushroom. Clearing an Excitebike Event Course is necessary to unlock the costume. Here, the costume is simply named "Bike."
Super Smash Bros. Melee
Super Smash Bros. Brawl
Super Smash Bros. for Nintendo 3DS / Wii U