Great Cataclysm

The Great Cataclysm was the moment when Ganondorf, the Gerudo King of Thieves, laid his tainted, blood-stained hands on the Triforce for the first time after finding the entrance to the Sacred Realm and transformed the Realm into the Dark World. The Dark World reflected Ganondorf's heart, and turned into a world of darkness and despair. Based on Ganondorf's inner self, he was transformed into Ganon, the King of Evil and Prince of Darkness.

On Cataclysm's Eve
"The Hero's triumph on Cataclysm's Eve wins three symbols of virtue. The Master Sword he then retrieves, keeping the Knight's line true."

- Pedestal of Time, The Legend of Zelda: A Link to the Past

"I am Aginah. I sense something is happening in the Golden Land the Seven Wise Men sealed... This must be an omen of the Great Cataclysm foretold by the people of Hylian blood..."

- Aginah

"Do you know the prophecy of the Great Cataclysm? This is the way I heard it... If a person who has an evil heart gets the Triforce, a Hero is destined to appear... ...and he alone must face the person who began the Great Cataclysm. If the evil one destroys the Hero, nothing can save the world from his wicked reign. Only a person of the Knights of Hyrule, who protected the royalty of Hylia, can become the Hero...You are of their blood-line, aren't you? Then you must rescue Zelda without fail."

- Maiden in the Skull Dungeon

Theories Surrounding the Great Cataclsym
According to ALttP, the Great Cataclysm occurred when the Gerudo King of Thieves, Ganondorf, entered the Sacred Realm (or Golden Land) and seized the sacred Triforce for himself. The Great Cataclysm then led to a prolonged and bloody conflict known as the Imprisoning War that resulted in Ganon's (as Ganondorf came to be called) "imprisonment" inside the Sacred Realm, which became the Dark World due to his vile influence. These events were chronicled in The Legend of Zelda: Ocarina of Time, when the Hero of Time pulled the Master Sword from the Pedestal of Time and opened the gateway to the Sacred Realm. In doing so, he was sealed in the Sacred Realm for seven years, and Ganondorf used the gateway he opened to enter the Sacred Realm, claiming the Triforce with blood-stained hands. The "three symbols of virtue" the Hero supposedly won were the three Spiritual Stones (which possibly became the Pendants of Virtue centuries later). The Hero's heritage "keeping the Knights' line true" seems to indicate that the Hero of Time, the Hero at the time of the Great Cataclysm, was a descendant of the Knights of Hyrule. If this is so, it would lend credence to the possibility that the Link from ALttP is a descendant of the Link from OoT since the one from ALttP was noted as being the last of the bloodline of the Knights of Hyrule.