From the Super Mario Wiki
Mushroom Trampolines, also simply known as "mushroom platforms" and "toadstools", are a type of platform that appear in several Super Mario games as well as the Mario Kart series. As they are trampolines, the player will bounce while standing on them, similar to a Note Block or Springboard. In the platformer games, holding down the button when the player jumps results in a higher jump.
Super Mario series
New Super Mario Bros.
Debuting in New Super Mario Bros., Mushroom Trampolines appear most prominently in World 1-5, but also appear in World 1-3 and World 7-4. In this game, they are pink with lighter-colored spots and will bounce the player even higher if they press the jump button at the correct time.
New Super Mario Bros. 2
Super Mario 3D Land / Super Mario 3D World
Mushroom Trampolines also appear in Super Mario 3D Land and Super Mario 3D World, serving the same purpose as in the 2D games. In these games, they are orange with yellow spots, and only a few of them have stalks.
Mario Kart series
Mario Kart Wii
In Mario Kart Wii, the cave section of Mushroom Gorge features multiple Mushroom Trampolines, which racers must bounce on to traverse the bottomless pit. Additionally, bouncing off Mushroom Trampolines allows the racer to perform Tricks. Only the red mushrooms are Mushroom Trampolines, however, as the green ones are Mushroom Platforms and do not bounce racers up. Many Mushroom Trampolines can also be seen in the background in the cave.
Mushroom Trampolines were also featured in tournaments. For the second tournament of July 2009, many Mushroom Trampolines were placed on Yoshi Falls. The player had to bounce over sections of water to complete the track. For the first tournament of April 2010, the player had to bounce around Mushroom Trampolines in the middle of the sea in Peach Beach.
Mario Kart 7
Mushroom Gorge returns in Mario Kart 7, although in this rendition of the course, one red Mushroom Trampoline is replaced by a blue-colored one, which not only bounces the racer up, but also triggers the kart's Glider in a similar fashion to a blue Boost Pad. A single Mushroom Trampoline also appears on Mario Circuit, and a rainbow-colored one appears on Rainbow Road, which serves the same function.
Super Smash Bros. for Nintendo 3DS
The Rainbow Road track from Mario Kart 7 appears in Super Smash Bros. for Nintendo 3DS as a stage, which includes the Mushroom Trampoline. However, unlike in the original game, it isn't bouncy and merely acts as one of the main platforms of the stage. It also has no effect on the Shy Guys that drive over it.
Mario and Sonic at the Sochi 2014 Olympic Winter Games
In Mario and Sonic at the Sochi 2014 Olympic Winter Games, Mushroom Trampolines appear in the Dream Event, Snow Day Street Hockey (Market Street).