Fez

A Fez is a type of hat with the shape of a truncated cone. The Doctor took a fez off an exhibit in the museum where the Pandorica was, and put it on, wearing it as he leapt back and forth through time. He stated that "fezzes are cool", in the same way he often states that "bowties are cool". It was taken from him by Amy Pond and destroyed with a gun by River Song. When the Doctor awoke after using the Pandorica to undo the destruction of the Universe, he was disappointed to not be wearing a fez anymore, but concluded that he could buy a new one. 

Behind the scenes
Steven Moffat said that Matt Smith grew fond of the fez so they had to destroy it to stop him from insisting on wearing it next series. Matt Smith had also once said that he hoped the costume evolved to include a hat.