Mario Cap
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Mario's Hat is an important part of Mario's clothing. His hat has an red M symbol. This hat has appeared in every game with Mario (Except the Dr. Mario series). Mario was even born with it!
The first game where it was important was Super Mario 64. There were many ways Mario could lose his hat, among them having it stolen by a Ukiki, and when he did lose it, he took more damage. The same happened in Super Mario Sunshine, and is presumed to occur again in upcoming Super Mario Galaxy.
By taking advantage of certain glitches in the game, Mario could end up with more than one hat in Super Mario 64. Mario could use the duplicate hat as an effective weapon.