The custom of trick or treating has several origins according to an article I've read at halloweenishere.com. During Samhain, the ]]Druids]] believed that those who pass away would play trick on people and cause panic and destruction. There is a need to appease them so country folks would give the Druids food as they visit their homes.

An old Irish peasant practice called for going door to door to collect money, breadcake, cheese, eggs, butter, apples, etc in welcoming the festival of St. Columb Kill.

A 19th century European custom called souling where early Christians would walk from village to village begging for "soul cakes" made out of square pieces of bread with currants. The more sold cakes the beggars will receive the more prayers they would promise to say for the dead relatives of the donors. It was believed at that time that the dead remained in limbo for a time after death and that even prayers done by strangers could help a souls fast passage to heaven.

Nobody is actually really sure. Halloween itself comes from a pagan holiday called Samhain. Samhain was the day they felt that the space between the living and the dead realm so to speak was at its thinnest. They held feasts and lit fires to honor the dead, but they also dressed up in costumes so the dead wouldn't know them to possess their bodies. Food from the feasts was also said to be left in plates for the dead. Some feel this offering of food is where trick or treating got it's start.

Another story is that the space between the magic realm and our realm is also thin on Halloween and that fairies and other fae would pass into our realm pose as street people and knock on doors for food. If they were not given a treat they would play tricks on the home owners as fairies are well known for the mischief.

Yet another story is that trick or treating evolved from England where children would go door to door collecting soul cakes. Anytime a child was given a cake they would say a prayer to a dead loved one for the giver.

A full article covering more of Halloween's history as well as some other Halloween trivia:
http://www.associatedcontent.com/article/931263/halloween_history_and_recipes.html?cat=22