Greek tradition has it that this practice started when a rich family invited a much poorer family to dinner and to make them feel better invited them to break the plates. They were proving that friendship is everything. And there�s no better way of proving that than dining with friends over Greek food.
In its earliest form, plate smashing may be a survival of the ancient custom of ritually "killing" the ceramic vessels used for feasts commemorating the dead. The voluntary breaking of plates, which is a type of controlled loss, may also have helped participants in dealing with the deaths of their loved ones, a loss which they could not control. [source About.com]
They throw carnations to singers, and smash glasses and dishes when beautiful girls dance the zeibekiko or the hasapiko on the dance floor. Back in the '30s they used to throw knives, a sign of respect and manhood, at dancers' feet. Due to countless injuries, that tradition gradually changed to the present-day plate-throwing tradition. [source Athens info guide]
Modern Greeks hold the custom in some disdain. "Nobody breaks plates, as a sign of kefi anymore, people throw flowers instead.