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Peach's Parasol (also called Peach's Umbrella) is what Princess Peach uses to defend herself and to glide in the air. It replaces her floating dress ability from Super Mario Bros. 2. Peach has been using this parasol ever since she was a baby.
Super Mario RPG: Legend of the Seven Stars
Super Mario series
Super Mario Sunshine
Princess Peach uses this parasol in Super Mario Sunshine to protect her from the dangerous heat and she is also seen floating down with it in the ending.
Super Mario Galaxy 2
Super Mario 3D Land
Super Mario Maker
Super Princess Peach
The parasol Peach uses in Super Princess Peach actually has a mind of its own. It is implied in-game that this parasol was once a human being until two sorcerers' magic transformed him. She can whack enemies with him and give him various upgrades. Perry can even eat enemies to refill the Vibe Gauge.
Paper Mario series
Super Paper Mario
The parasol appears in Super Paper Mario, where Peach can use it to float and defend herself while crouching.
Paper Mario: Color Splash
In Paper Mario: Color Splash, Peach can be seen holding the parasol when she first arrives at Port Prisma, along with in official artwork for the game. In the digital manual, when asked where she keeps the parasol, Peach claims that it is none of the viewer's business.
Yoshi's Island DS
Mario Party 3
Mario Kart series
Mario & Luigi: Dream Team
In Mario & Luigi: Dream Team, the parasol makes a cameo in the credits.
Super Smash Bros. series
The parasol appears in Super Smash Bros. Melee where it is a special move. She can glide in the air with it and hit opponents. It also appears in Super Smash Bros. Brawl and Super Smash Bros. for Nintendo 3DS / Wii U, with the same function and its Super Paper Mario design.
In Super Smash Bros. for Nintendo 3DS / Wii U, two additional variations are added, Parasol High Jump and Light Parasol. Parasol High Jump has her jump high, but she does not float with the parasol, making her helpless after the jump. Light Parasol decreases the initial jump height, but every time she opens the parasol, she can slightly glide upward. After this sequence has been performed four consecutive times, she becomes helpless.