From the Super Mario Wiki
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Mushroom Platforms are semi-solid platforms that are shaped like a mushroom. These platforms were introduced in Super Mario Bros. in the Warp Zone in World 4-2, where they were initially solid platforms. Mushroom Platforms have since appeared in most Mario games.
In the Yoshi's Island series, Mushroom Platforms first appear in Super Mario World 2: Yoshi's Island. In this game, Mushroom Platforms appear in cave levels, with many having much thinner stalks and caps, which curve around more than the blocky squarish ones from most Mario games. They come in multiple colors, such as red, blue, beige, and purple, and have a whitish center area instead of spots. Thicker ones with triangular caps also exist, and do have spots. Smaller examples of these can come in other colors, such as dark mahogany and dark pine green, while even smaller than that are limited to blue, red, beige, and purple, like the largest ones. Most of both types appear to have a slice out of the cap, but the smaller two versions of the latter type lack these.
In the Mario Kart series, Mushroom Platforms first appear as a cameo in the background of Mario Circuit in Mario Kart: Double Dash!!. Mario Kart Wii features a track themed after them, Mushroom Gorge. Green Mushroom Platforms are standard platforms, while the player can bounce off the red Mushroom Platforms, and can glide off of blue Mushroom Platforms, the last of which only appears in the Mario Kart 7 Retro Course.
A similarly-themed object known as a Mushroom Trampoline that appears in Super Mario 3D Land and Super Mario 3D World act similarly to the red Mushroom Platforms from the Mario Kart series. In these games, they are colored orange with yellow spots.
Mushroom Platforms also appear in the Golden Plains and Rainbow Road stages in Super Smash Bros. for Nintendo 3DS. The ones in the former stage are semi-soft platforms, while the one in the latter is not, as it is one of the stage's main fighting arenas.
Mushroom Platforms appear as placeable objects in Super Mario Maker and Super Mario Maker for Nintendo 3DS. Their height and length can be adjusted in the level editor. When Mushroom Platforms are placed underwater, their appearance changes to resemble coral. When they are placed in Airships in all styles except for New Super Mario Bros. U, their appearance becomes more metallic.