Princess Peach's Crown
From the Super Mario Wiki, the Mario encyclopedia
Princess Peach's Crown, also called Princess Peach's tiara, is Princess Peach's emblem and a symbol of the Mushroom Kingdom. The only significant role it has played is being a lost object that must be retrieved. A majority of the time, the crown never leaves her head, aside from a few occasions, no matter how violently or quickly Peach moves around.
In the Nintendo Comics System issue Cloud Burst, Princess Peach has lost her crown and needs it for her yearly recoronation, so she sends Mario and Luigi to retrieve it. She believes King Koopa to have stolen it as he is invading "World 3". In reality, it was stolen, along with King Koopa's crown, by a Lakitu and the plumbers eventually get it back for her.
In Super Mario RPG: Legend of the Seven Stars, Princess Peach loses her crown during her wedding to Booster and Mario has to find it. Mario eventually finds the crown on top of Booster's head. Depending on how fast Mario finds this and a bunch of Princess Peach's other items, he may receive a kiss from Peach (if he does it very slowly, Booster, Bowser, or even both may kiss him).
In the Super Smash Bros. series, Peach attacks in her forward aerial by swiping down with her crown before putting it back on.
Throughout most of Super Mario Odyssey, Peach is seen to be wearing a tiara which is revealed to be Cappy's sister, Tiara, rather than her crown. In the post-game, after her adventure, Peach is back in her regular usual dress and is back to wearing her usual crown.