There are many families related with Harry Potter. He being a person who has the power of love and affection(which tom lacks) has a lot of families to his support.Many of them are ready to give their lives to save Harry.
The main family he is associated with is the Potter Family but sadly he has no living relations in his own family.
Of all the families the Weasleys are the best and he gets associated with them in the end making a one happy weasley potter family.
Though he had very little exposure with the blacks he has both love and enemity from the same family ie from sirius (love of a Godfather) and the hatred of Bellatrix lesrange and Narcissa malfoy.