The most common hat throwing tradition seems to be at high-school and college graduations with the mortarboard hats. The congratulations are issued, everyone moves the tassel from one side to the other and zing! Off go the hats.
When a baseball player hits a game-winning home run, he will toss his helmet. When the San Francisco Giants recently won the World Series, they tossed their hats in the air. Football players are penalized for throwing or even removing their helmets on the field after one too many errant celebrations and taunting incidents in recent history.
When a hockey player manages to score three goals in any one game, it is called a hat trick, and in the National Hockey League, the expectation is that everyone in the stands removes their hat and tosses it onto the ice, creating quite a spectacle, and quite a mess. In an array of professional sports, when the referee has been deemed to make an odious and detrimental call, fans will sometimes rain down hats onto the field, court or playing surface, temporarily halting the game. In fact many people have been known to toss their hat or cap in a fit of rage when in an argument with a significant other, street vendor, or the like.
The screen villain Oddjob, of James Bond fame had a lethal hat fitted with a blade which he would throw, decapitating his targeted aggressors. The hat ranked tenth in a recent 20th Century Fox poll of the most popular film weapons of all time.