Straw Hat

A straw hat can refer to any brimmed hat that is woven out of straw. This hat is designed to protect the head from the sun, as well as protect against heatstroke.

There are several styles of straw hats, but all of them are made of woven straw. Many of these hats are formed in a similar way to felt hats; they are softened by steam or by submersion in hot water, and then formed by hand or over a block. Finer and more expensive straw hats have a tighter and more consistent weave. Since it takes much more time to weave a larger hat than a smaller one, larger hats are more expensive.

History
Straw hats have been worn consistently in Europe in the Summer since antiquity, and arguably are the least-changed form of headgear, since many medieval examples would draw no special attention if worn today. Many are to be seen in the famous calendar miniatures of the Très Riches Heures du Duc de Berry, worn by all classes, mostly by men. The Middle Ages also produced, among the more fashionably dressed, possibly the most spectacular straw hats ever seen on men in the West, notably those worn in the Arnolfini Portrait of 1434 by Jan van Eyck (tall, stained black) and by Saint George in a painting by Pisanello of around the same date.

One Piece
In the manga and anime One Piece, Monkey D. Luffy's straw hat is the main symbol of the entire series and is the origin of his nickname "Straw Hat Luffy." His straw hat was given to him by his idol, Red-Haired Shanks when he was a kid, and he promised to give the hat back to him once he becomes a great pirate (or in other words, the new Pirate King).

Although Luffy's straw hat is his treasure, he is seen without it on occasion. This is usually because he doesn't want anything bad to happen to it. In which case, he usually gives it either to Nami or Usopp for safe keeping. If it ever does get damaged (i.e., Buggy cutting it by stabbing it with his knives), Luffy becomes furious and he becomes extremely depressed if he loses it. Nami is usually the one that repairs it.

During the Arabasta arc, when Ace leaves the Straw Hats and Vivi, he gives Luffy a "blank piece of white paper" (Vivre Card). Saving it from getting eaten by Eyelashes, Nami sews it under the red rim of his hat.

Luffy's hat fell off when Jinbei, who was carrying him, was struck by Admiral Akainu. As Luffy was mentally shattered from his brother's death, he did not notice, nor did Jinbei, who was occupied with dealing with the Admiral. After Shanks appeared, the straw hat was reunited with its old owner after over 10 years. Shanks convinces Buggy to return the straw hat to Luffy shortly after, and ended up in Trafalgar Law's temporary care. It was then handed over to Silvers Rayleigh, who in turn returned the straw hat to Luffy after he recovered. Prior to his two-years training with Rayleigh at Rusukaina island, Luffy set aside the hat at the island's only safe location. He eventually picked it back up after the training is over.

Fake Luffy's Straw Hat
Fake Luffy, in a poor attempt to impersonate the real Luffy, also wears a straw hat. However, his was different by being frayed and unkempt, and having a stripped band around its circumference. This differs from the real one, as though he did not care at the very least to its well being. It fell off when Sentoumaru smashed him on the head.

Trivia

 * Luffy's straw hat has somehow managed to survive through all his battles even when it logically couldn't possibly have, as when he was poisoned by Magellan and was literally melting.