The first thing that must be understood is that time is not always a straight line. There are certain points in history at which the timeline can be bent. If the timeline is bent in certain ways, it can close in on itself. This creates a time loop in which history perfectly repeats itself, and those involved remain completely unaware.

In Hyrule, time has three corners. Three corners has its time. And had it not three corners, it would not be...

The Triforce of Time Theory (TToTT)
By SteveT, Masamune, and Luigi of the Pipes

(Note: This theory follows Link's life. Due to reasons explained, his life spans multiple iterations of the timeline. We will look at each iteration individually. Bear in mind that the events of all three iterations happen in a single iteration for all observers other than Link. We choose the lower left corner as an arbitrary origin.)

First Iteration

It all started when the Hero of Time, Link, was born. This event marked the first convergence of two sides of the Triforce of Time.

Link's mother, Princess Zelda, held ancient future knowledge regarding the whereabouts of the Triforce of Courage, and her jealous brother demanded it from her. Meanwhile, war broke out in Hyrule. In the strife that followed, Zelda deposited her son with the Great Deku Tree, who raised him as a Kokiri. Zelda herself, as told in the Adventure of Link back-story, was put to sleep by a wizard in her brother's employ. Although the wizard certainly had not planned it this way, Zelda slept backwards through time, rejuvenating as she did so (this will make sense later).

Eventually, Ganon came to Hyrule. Link then became involved in the familiar plot of Ocarina of Time. With Ganon sealed in a prison that transcended time, Link was free to relive those seven years in the comfort of the Kokiri woods. In fact, he resided there much longer than seven years, and prolonged exposure to Deku Tree magic combined with Princess Zelda's (not the same as the sleeping Zelda, obviously) rejuvenating spell permanently slowed Link's rate of aging, even after he left the Kokiri forest. (Ocarina of Time)

Link then was lured into Termina by the Skull Kid. There, he saved Termina, and in a feat of dramatic irony completely failed to realize that just as Termina was locked in a time loop to prevent its own destruction, Hyrule was in a much larger time triangle to prevent its salvation. This irony was not lost on Tingle, as shall be shown. (Majora's Mask)

Due to the unpredictable nature of inter-dimensional travel, when Link left Termina, he found that Hyrule had long ago been destroyed and was now a system of islands. (Not that he remembered Hyrule. Link was a chronic amnesiac—the rejuvenating spells affected his mind as well as his body.) He was adopted by a kindly old woman, who took mercy on this homeless piece of driftwood. He lovingly referred to her as “grandmother” and partook of her excellent soup. Soon enough, Link found himself on a pirate ship on a quest to save his “sister”. Soon enough after that, he was on a quest to stop Ganon from stealing the Triforce.

The King of Red Lions and Jabun explicitly stated that this Link was not the Hero of Time. Shows what they know.

Anyway, Link defeated Ganon, but not entirely. Ganon, the Villian of Time, had the favor of the goddesses. It was their wish for Hyrule to be lost beneath the sea. Here, the timeline would have straightened. However, King Hyrule's final wish was to bring hope to Hyrule. That hope could only be achieved in one way: by repairing the past. (The Wind Waker)

While the Triforce was thinking about a plan, Link sailed off with Tetra's crew, got caught in a storm, and probably had a lucid dream (or maybe not!).  I don't really know what was going on there. (Phantom Hourglass)

Later on, the Triforce yanked Link from the new land he would have settled, and dropped him at the doorstep of a friendly knight of Hyrule centuries earlier. The knight took in the boy with no memory, and Link became fond of him, and called him his uncle.

Unbeknownst to Link, he had arrived in Hyrule just before Ganon had freed himself to wreak the havoc that resulted in the flooding of Hyrule. As chronicled in Link to the Past, Link averted this disaster by preventing Ganon from ever escaping the Dark World. This completed the right-hand corner of the triangle. (A Link to the Past)

Link's uncle became a blacksmith, and on the day he sprouted his first grey hair, Link began to call him “grandpa.” Having already forgotten the events of LttP, Link embraced the power of the Four Sword to defeat the upstart wizard Vaati, with the aid of his new ally, Ezlo. (The Minish Cap)

Thereafter, Link began to wonder why he did not age like the other people of Hyrule. As if to prevent him from realizing who he was, the Triforce intervened and sent him on a quest in the distant lands of Holodrum and Labrynna. Distant in the future, that is. (Oracles)

The Oracle games constitute another corner of the Triforce of Time. Had Link not prevented the resurrection of Ganon, Ganon would have again succeeded in straightening the timeline, and many a good thing would have failed to happen.

After bending time once more, and forgetting who he was once more, Link used the Four Sword to defeat Vaati again. Twice. The second time, he encountered Ganondorf for the first time. That is to say, Ganon was born on this side of the triangle. (Four Swords, Four Swords Adventure)

After this, Link engaged in his ancient hobby of sailing. He was summarily shipwrecked. The goddesses had sent a vicious storm in their anger over their timeline being turned into a triangle. Their plan failed, however, and Link found himself in the mind of the Wind Fish, where he defeated the Nightmare. The Wind Fish, however, had slumbered for centuries from the point of view of Hyrule, and by the time he awoke, and consequently by the time Link returned to reality, centuries had passed. (Link's Awakening).

Hyrule had changed so much that Link could hardly consider himself a citizen of it, assuming he even knew who or where he was. His first action was to save an old woman named Impa from a group of Moblins. She begged him to collect pieces of the Triforce of Wisdom and defeat Ganon, which he gladly did, since he didn't really have much going on at the moment. (The Legend of Zelda)

He then went on to awaken the sleeping Princess Zelda, who after her slumber back through time was a young woman again. (The Adventure of Link)

Link married Zelda and helped rebuild Hyrule. Nine months later, the timetrangle converged, and Link was born.

Second Iteration

The shock of becoming his own father was too much for Link. Deciding he need to find himself, Link abandoned his family and wandered Hyrule for decades, eventually settling in the Ordana province. He became a rancher, until Zant's minions attacked his village. Enslaved by Midna, he set off to defeat Zant and restore order. As it turned out, Zant was just a pawn of Ganon, so Link fought him, too. (Twilight Princess)

In the coming months, Link's amnesia finally began to fade. Link became obsessed with fairies, slouched until his height diminished, gained a few pounds, and adopted the name “Tingle,” after the sensation he felt whenever an old memory came back to him.

He resolved to spare himself the pain and suffering that he had experienced, and chased his son, hoping to hinder his every quest with minor annoyances, such as charging too much for maps or distracting him with entertaining games like “hammer tag.”

Sometime before Link to the Past, Tingle came across the Four Sword. He used it and split into four Tingles. They remained separated and kept the Four Sword, calling themselves the Tingle brothers (Tingle, Ankle, Knuckle, and David Jr.). They toured Hyrule, annoying Link at every opportunity.

Tingle died sometime after The Adventure of Link, and his blood was used to revive Ganon, thus beginning the events of Ocarina of Time. But Tingle did not entirely die. Since he was still split into four, the Magic of the Four Sword kept his spirit alive. His ghost(s) remained in Hyrule.

Third Iteration

Link/Tingle's ghost desperately hoped to prevent himself from coming into existence. First, he appeared to Link as the Undead Warrior in Twilight Princess. He hoped that his lessons would help his younger counterpart to retain his sanity. When this failed, he decided to try more desperate measures. He waited for Link to appear at the Pyramid of Power (LttP GBA) and tried to murder his younger self.

Fate would not be cheated, however, and Link defeated the Four Tingles, finally laying his own spirit to rest.

Frequently Asked Questions

Q: What does “iteration” mean?

A: It's roughly synonymous with “repetition.”

Q: Why doesn't anyone other than Tingle know they're trapped in a time loop?

A: First, because this time loop resets after thousands of years, and no one has that kind of long-term memory. Second, because it's pretty clear that Hyrule was in something of a Dark Age during the NES games. Most of its culture, history, etc. was lost. A better question is: Why would anyone know?

Q: Is the Triforce of Time a physical object like the other Triforces?

A: Not at all. Since the timeline of Hyrule is in fact, triangular, and this theory is golden, we felt “Triforce of Time” was a fitting way to describe it.

Q: Was there a timeline in which Tingle did not appear? That is, does an “original” time loop exist?

A: Probably not. After all, realizing he would become Tingle was half of what drove Link to the madness that caused him to become Tingle in the first place. You'd do the same thing, trust me.

Q: So you're saying Zelda slept backwards in time? How does that work, exactly?

A: A wizard did it.

Q: But wouldn't it make more sense if she slept all the way around the Timeline and is then awakened a few years before her younger self is put to sleep?

A: The shortest distance between two points is a single line. Zelda sleeps backwards in time because it takes less time to get to that point as opposed to going around the entire triangle. It's basic geometry, people.

Q: Are all the Zeldas the same person, too?

A: No. In a given loop, there are roughly one Zelda per two games (give or take). Zelda is a glitch in the Triforce of Time, and is repeatedly reincarnated as an identical person. A similar effect occurs with other figures, no doubt due to the inherent instability of a triangular timeline.

Q: In Majora's Mask, Tingle's father is the burly tour man, but you say that Link is both Tingle and his own father. Explain yourselves!

A: That particular Tingle was the Termina version of Link.

Q: Isn't it biologically impossible for Link to be his own father? The genetics of it!

A: Isn't it biologically impossible for a wombat to grow a steel helmet?

Link's genetic situation is not impossible (albeit unlikely in a low-magic setting such as ours), so long as 50% of Zelda's DNA is identical to Link's. Remember, Zelda isn't just his wife. She's also his mother. They obviously share a lot of genes.

In any event, this type of thing is why incest is illegal.

Q: What about TML's Song of Storms paradox?

A: I don't have to answer this. TML officially endorses TToTT in his article.