The Single Link Theory 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. 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".
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.