The Single Link Theory (actually called the "One Link Theory" by those who held this position and actively debated online in its favor) is an idea that was widely accepted by Zelda fans until 2003, just before the release of The Wind Waker. The theory states that there is only one Link in all the games in The Legend of Zelda series. According to this theory, each game is a separate adventure in a single Link's lifetime. Just as the Split Timeline is widely accepted today, the Single Link Theory was one of the most commonly believed theories of its time. However, before the release of The Wind Waker in 2003, Shigeru Miyamoto confirmed in an interview with Nintendo Power that there are multiple Links throughout the series. Some believe that the release of The Wind Waker put an end to the Single Link Theory, as the prologue of the game references the Hero of Time, while the protagonist of the game was given the title "Hero of Winds". However, the theory did not end here. The One Link Theorists at the time contended that The Wind Waker took place within a "what if" timeline. That is, what would have been if Link had stayed in the adult timeline rather than traveled back in time at the end of Ocarina of Time. The contention was that because Link did go back in time, it meant that the future events were erased and overwritten by the child timeline which included Majora's Mask. This was known as the "Erased Timeline Theory", in opposition to the Split Timeline Theory. Therefore, the events of The Wind Waker never took place, and thus there was still only one Link. It was however speculated by One Link Theorists at the time that Eiji Anouma might eventually lead the series in a different direction from Shigeru Miyamoto's stated timeline that consisted of one Link across the original games in order of their release except with Ocarina of Time being placed first in the timeline and Link's Awakening being placed afterward at any point in the series.
The theory was only truly retired with the release of Twilight Princess, in which an obviously new Link was featured with events referring to the child timeline of Ocarina of Time. It became clear that Eiji Anouma and Shigeru Miyamoto would apply the concept of multiple incarnations of Link to every timeline and continue the concept in future releases. Hence the theory was retired.
Today, the idea that there are multiple Links throughout the series is widely accepted, and most modern timeline theories contradict the Single Link Theory. Some believe that all the Links are descendants of the Hero of Time, the protagonist of Ocarina of Time. To many Zelda fans, the Single Link Theory is an impossibility, and is rarely mentioned.
Because some people believe that The Legend of Zelda: The Minish Cap came first in the series, some people also think that each Link or some Links are descendants of the Hero of Men, rather than the Hero of Time.
Hero's Spirit Theory
It should be noted that it is still possible that the Single Link theory may be valid, if one considers each incarnation of Link to be reincarnations/past lives of the same soul. The idea that each one is the reincarnation of the Spirit of the Hero is even used in the plot of the non-canon Hyrule Warriors series, to explain the various incarnations of The Hero Link within that universe (which is officially separated from the main universe). While the Hero's Shade and Link's appearance in Twilight Princess may seem to contradict this idea, it is possible that Hero's Shade is Link's previous incarnation the Hero of Time, who spirit wishes to pass on his knowledge to his certain incarnation, allowing the Hero of Time's spirit to achieve inner peace. It is also possible that due the Hero of Time being sent back in time, the cycle of reincarnation was interrupted, preventing another incarnation of Link appearing when Ganon escaped in the Adult Timeline, resulting in the Great Flood, though eventually was reincarnated into the Hero of Winds and then the Link from Spirit Tracks.
Order of the Games
The order of the games within the One Link Theory varied slightly between different theorists, but because One Link Theorists touted themselves as strict adherents to the facts of the games as well as to Shigeru Miyamoto's statements, most agreed that the Miyamoto Order was the best basis for the theory, and the most likely to be deemed official.
The One Link Theory also draws from the Single Link Timeline, though this timeline was from Nintendo of America and moves the placement of A Link to the Past to before the NES games. The Miyamoto Order takes precedence in the One Link Theory.
The order for most One Link theories is: Ocarina of Time, The Legend of Zelda, The Adventure of Link, A Link to the Past, and Link's Awakening.
Miyamoto stated that Link's Awakening could be placed anywhere after Ocarina of Time. Most One Link theorists placed Link's Awakening at the end of the timeline due to the final boss of the game taking the forms of Agahnim and Ganon from A Link to the Past. This suggested that the Nightmare saw Link's memories of these enemies and assumed their forms, and thus Link's Awakening must take place after A Link to the Past, which Miyamoto placed after the NES games.
The placement of Majora's Mask directly follows Ocarina of Time.
Theorists debated the placement of the Oracle games, as the inclusion of what appeared to be the Triforce gave conflicting opinions. Some said the Triforce's inclusion would have to place the Oracle games after A Link to the Past in which Link united the Triforce parts and developed the ability to touch the Triforce without the parts splitting up as they did with Ganondorf in Ocarina of Time. Some theorists said the scenes involving the Triforce were just visions or dreams of prophecy Link had of one day claiming the complete Triforce, which would later happen in A Link to the Past. These theorists placed the Oracle games before A Link to the Past.
Further theorizing also placed the Oracle games after Majora's Mask, but before the NES games due to Link appearing to be younger than the art depicted in the NES games but older than the art depicted in Majora's Mask.
All One Link Theorists were certain on one subject however. The Wind Waker took place in the future timeline of Ocarina of Time, and this future was erased when Link went back in time. This was called the Erased Timeline Theory.