This is one of the arguments that has raged on since the launch of the first game, Some the very beginning of the Legend of Zelda series. It is called the Multiple Links Theory. And it is about how many Links there are in the series. So I have devised three options as to how many Links there are. And here they are:

Some say that there are many Links throughout the series. I believe in this theory the strongest, and so I have made a list of all of the Links recorded throughout Hyrulian legend based on this theory:

The Adventure of Link (the intro part where Princess Zelda is put to sleep by the wizard): No Link in story
The Ocarina of Time: Link I
Majora's Mask: Link I
Twilight Princess: Link II
The Wind Waker: Link III
Phantom Hourglass: Link III
Oracle of Seasons: Link IV
Oracle of Ages: Link IV
Link's Awakening: Link IV
The Minish Cap: Link V
Four Swords: Link VI
Four Swords Adventure: Link VII
A Link to the Past: Link VIII
The Legend of Zelda: Link IX
The Adventure of Link: Link IX

2. Others say that every game features the same Link as the game before it. This theory cannot be true because in The Wind Waker, it clearly states that the hero clothed in green (in the intro to the game) is the Hero of Time. And everyone knows for a fact that the Hero of Time is Link in the Ocarina of Time, so the Link in The Wind Waker must be a different Link than the one in Ocarina of Time, proving this theory wrong.

3. Some people also believe that each story is just a retelling of the original story (Ocarina of Time) with slight modifications each time. I do not feel so strongly about disproving this theory because it might as well be true. Each story is almost always connected with each other, but there are weak spots. One is my Wind Waker point, that proves two separate stories, but also just might be added details. Another is Link's Awakening, for it had nothing to do with the series and had no connection with any other Legend of Zelda games, but it does hint that it might all have been a dream, therefore making it not a story in the series and making this theory possibly true. You pick which theory you want to believe.

Here is an old theory of ours. Some believe it may be correct, but I have since changed the timeline theory that this Links theory depended upon.

The Adventure of Link (the intro part where Princess Zelda is put to sleep by the wizard): second Link
The Ocarina of Time: first Link
Majora's Mask: first Link
The Wind Waker: third Link
The Legend of Zelda: fourth Link
The Adventure of Link (the main part): fifth Link
Oracle of Seasons: sixth Link
Oracle of Ages: sixth Link
Link's Awakening: seventh Link
The Minish Cap: eighth Link
Four Swords: ninth Link
Four Swords Adventure: tenth Link
A Link to the Past: eleventh Link