Sainthood isn't the sort of thing that runs in families, per se, but there are still families in which one finds it concentrated. One of the most famous of these was the family of St. Basil the Great of Caesarea, which had a hefty number of saints all at once: St. Basil was brother to St. Gregory of Nyssa and St. Macrina, and they were three out of ten of the children of St. Basil the Elder and St.Emmelia, and St. Basil the Elder was the son of two confessors, one of whom was St. Macrina the Elder, while St.Emmelia was the daughter of a martyr. Another family that also had an unusual concentration of saints, although not all at once, was the Árpád dynasty of Hungary, from which that royal family got the nickname, Family of the Saint-Kings. The saints in question were:
King St. Stephen I, Founder of Christian Hungary
Prince St. Emeric (who was also related on his mother's side to King St. Henry II of Germany, after whom he was named; the word 'America' ultimately comes from his name, by way of Amerigo Vespucci)
King St. Ladislaus I
Empress St. Irene of Hungary (who was born Piroska, was the daughter of Ladislaus, and married Emperor John II Komnenos)
Princess St. Elisabeth of Hungary (who was also related on her mother's side to High Duchess St. Hedwig of Andechs and Silesia)
Princess St. Kinga of Poland (Elisabeth's niece)
Princess St. Margaret of Hungary (Kinga's sister)
Blessed Jolenta of Poland (also Kinga's sister)
Today is the feast day of the most famous of the saintly Árpáds, Princess Elisabeth of Hungary. Widowed at age 20 as her husband, Ludwig IV, who was never officially canonized but is nonetheless still revered as a saint in some local calendars, died on the way to the Sixth Crusade, she devoted the next four years of her life to intensive charity for the poor: giving of alms, building of hospitals, and the like. She died at age twenty-four. She is the patron saint of hospitals, dying children, and the homeless.
(There should be more philosophical posts, by the way, as things get less busy around here.)