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.
The Adventure of Link
A Link to the Past
Ocarina of Time
When Link met Zelda as a young girl, Zelda told him of how her Father had trusted Ganondorf, and how she disliked his decision. While this is the only reference made, there is no defined other members of the family during this period in Hyrule.
Oracle of Ages/Seasons
Four Swords
The Wind Waker
Four Swords Adventures
The Minish Cap
Twilight Princess
In Twilight Princess, Zelda appeared to be the only living descendant of the Royal Family of Hyrule, depicted in the scene "The Invasion of Hyrule", when she is the only Royal Family member guarding the throne. It was also brought up that she made the decision to engulf Hyrule in Twilight rather then relinquish it, hinting that there was no higher power.