Link's Parents

Link's Father is the title given to the man who fathered Link, the Hero of Time. Not much at all is known about him, other than he is obviously deceased by the time of Ocarina of Time since Link is said to have been orphaned during the Hyrulean Civil War by the Great Deku Tree. However, he is mentioned in the unofficial manga of the game as having been a warrior that served the King of Hyrule before he unified the country in the Hyrulean Civil War. Rauru, the Sage of Light, tells Link that he was born into the guardian house that served the Hylian Royal Family at the time of the Hyrulean Civil War, implying that Link's father was one of the fabled Knights of Hyrule that served and protected the Royal Family. He also tells Link that his father was killed in battle before his mother brought him to the Great Deku Tree. This fits with the Hero's lineage spoken of in A Link to the Past, where the Pedestal of Time states that the Hero of Time "kept the Knights' line true" at the time of the Great Cataclysm. This implies that Link's father was one of the Knights of Hyrule, and that the Hero of Time was the last of their bloodline after the Knights were wiped out in the Imprisoning War. Hence, the most likely scenario from the Pedestal of Time's story in A Link to the Past as well as the manga of Ocarina of Time is that Link's father was indeed one of the fabled Knights of Hyrule that died defending the Hylian tribe during the Hyrulean Civil War.

Therories Surrounding Link's Father
The father of the Hero of Time can be traced back as far as A Link to the Past, where gamers first learn of the legends of the Master Sword, and its first master, the Hero of Time. The Pedestal of Time reads:

The Hero's triumph on Cataclysm's Eve,  ''wins three Sybols of Virtue.  The Master Sword he will then retrieve, '' ''keeping the Knights' line true. ''

The Hero of Time was the Hero at the time of the Great Cataclysm, and he won the three Spiritual Stones on the eve of the Great Cataclysm, when he unwittingly let Ganondorf into the Sacred Realm, where he shattered the Triforce. He retrieved the Master Sword and used it to fight alongside the Seven Sages during the Imprisoning War. The statement that he "kept the Knights' line true" implies he was descended from the Knights of Hyrule, who were wiped out in the Imprisoning War. As such, this implies that Link's father was that relative, and that he died defending the Hylian royalty.

This is further supported by the unofficial manga that accompanies the games. In the Ocarina of Time manga, Rauru, the Sage of Light, tells the grown up Link that he was indeed born into the house of guardians that protected the King of Hyrule and his family and that his father was one of those guardians. He goes on to tell Link that his father was killed in battle during the Hyrulean Civil War. This explains his absence in the game as well as the Hero of Time's blood link to the Knights of Hyrule, as stated by the Pedestal of Time in A Link to the Past.