Here is my theory about The Great Cataclysms that happen during the entire Zelda game series. A Great Cataclysm has two parts to it: Cataclysm's Eve, the day before The Great Cataclysm, and The Great Cataclysm itself. There are many sayings about The Great Cataclysm, and here are some of them:

The Hero's triumph on Cataclysm's Eve
Wins three symbols of virtue.
The Master Sword he will then retrieve,
Keeping the Knight's line true.
(These are the words written on the pedestal that houses the Master Sword in A Link to the Past. It is referring to the three pendants that Link must gather in Ocarina of Time, the Kokiri Emerald, the Goron's Ruby, and the Zora's Sapphire, to pull the Master Sword free from the pedestal.)

If a person who has an evil heart obtains 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 posses the power of the Winds, and who protected the royalty of Hylia, can become the Hero.
(These words can be found in Orca's writings - The Wind Waker)

Every time a Great Cataclysm happens, a hero is destined to appear.
(These are words spoken by an old lady that resides by the Lost Woods in A Link to the Past)

If you clear all of the dungeons of evil and win the Triforce, you will be recognized as the true Hero of Hyrule.
(Applies to The Legend of Zelda)

All of the above predictions describe a different Hero that can appear. The first prediction describes the Hero of Time, the second describes The Hero of Winds, and the third is the Hero of Cataclysm's Eve, and the fourth prediction talks about The Hero of Hyrule. There are 5 Great Cataclysms that occur throughout the entire series, and each has a certain Hero. Some of the Hero's names do repeat themselves, but they are not the same Links (see our Mulitple Links Theory page).

G.C. #1: The Hero of Time + The Hero of Hyrule + The Hero of Cataclysm's Eve (Ocarina of Time)
G.C. #2: The Hero of Hyrule (Twilight Princess)
G.C. #3: The Hero of Winds (The Wind Waker)
G.C. #4: The Hero of Hyrule + The Hero of Cataclysm's Eve (A Link to the Past)
G.C. #5: The Hero of Hyrule (The Legend of Zelda)