Hospitality plays a very big role in Greek life. It was by this system that people were able to travel without the fear of being rejected and having nowhere to stay. A host never knew if the beggar on his/her doorstep was a god in disguise. Such paranoia and religious beliefs kept most characters in Homer's Odyssey on the straight and narrow, but others had no manners to begin with.
In Greek religion travelers were protected by the head god: Zeus. He was supposed to take care of them and keep them safe while they were away from home. They, in turn, were to act in an according way. When welcomed into a house, one was supposed to be gracious and not demand more than the owner could give. Their stay was not to impose too much of a burden on the household, or the means of survival for that house. Rarely were visitors asked to leave, but if they were, the wishes of the host were to be satisfied. Basically, if a traveler was courteous and was not demanding, they were following the rules of hospitality laid down by the gods.
The owners of the household had other obligations. They were to welcome in whoever stepped on their doorstep. Whether it be a lowly beggar or the radiant image of Zeus himself, the leader of the house was to treat them well. Often times someone would show up and they would be welcomed in, fed, washed and then after a few drinks the host would ask the visitor what their business was in the area. Part of the motivation behind the supreme hospitality of the Greek culture had to do with the fear of the gods. There were stories of when the gods themselves would show up on a door step disguised as beggars and if they were not welcomed in the entire household would suffer. So really the hospitality is not always stemmed from complete goodness and out of kindness of heart, but also from the fear that they will make the gods mad.
In the Odyssey there are examples of well-behaved hosts and guests as well as those who could have used a lesson from the lightning bolts of Zeus.