Peach's Parasol (also called Peach's Umbrella) is what Princess Peach uses to defend herself and to glide in the air. In some games, it replaces and acts like 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
Her parasol first appears in Super Mario RPG: Legend of the Seven Stars, where it is a weapon able to be purchased from the shop in Seaside Town after Yaridovich is defeated, and colored blue. She earlier uses a different, pink one to sneak out of Mushroom Castle.
Mario Party 3
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, Super Smash Bros. for Nintendo 3DS / Wii U, and Super Smash Bros. Ultimate, with the same function and its Super Paper Mario design. In the Subspace Emissary in Super Smash Bros. Brawl, Peach briefly carries the parasol around while strolling on the Halberd's deck, and later gives it to a just-restored Mr. Game & Watch shortly after scolding him.
In Super Smash Bros. Ultimate, Daisy now owns a parasol identical to Peach's, albeit reused from Peach's alternate color in Super Smash Bros. for Nintendo 3DS / Wii U.
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.
Yoshi's Island DS
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. In later games, the parasol has retained its design from this game.
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.
Mario Kart series
Mario & Luigi: Dream Team
In Mario & Luigi: Dream Team, the parasol makes a cameo in the credits.
Mario Golf: World Tour
In Mario Golf: World Tour, Peach wields her parasol in her victory animation whenever she gets a Birdie or an Eagle. It is implied to be magical, as after waving her parasol around for a bit, she then swings it and has her miniskirt change into her trademark dress.
Mario + Rabbids Kingdom Battle