Royal Family of Hyrule
The Hylian Royal Family has been featured strongly in a few Zelda games, including Ocarina of Time and The Minish Cap. The most prominent member of the Hylian Royal Family is Princess Zelda, who appears in nearly every game. Several other members also appear across games, or are refered to.
The Hylian Royal Family is, in general, the most prominent of all leaders in Hyrule. They keep close contact with the other leaders or races/tribes as a whole
There is no current proven family tree or bloodline, due to a lack of information regarding Zelda's mother, or either of her parents parents. Without this information, it is impossible to construct a comprehensive family tree.
The Legend of Zelda
In The Legend of Zelda, the Hylian Royal Family was responsible for guarding the Triforce of Wisdom. When Ganon attacked, the young princess of Hyrule, Zelda, broke it into eight pieces and hid them, for which she was imprisoned by Ganon.