Why I Believe There is Only 1 Link:

[kroni]

The first and foremost reason that I believe there is only 1 Link is that ultimately it makes a better story. I'm not going to go into this further because it's subjective and people might disagree.

Second, if we do not believe there is one link, then we are forced to conclude that they are mere decendants. I could maybe accept one identical decendant, but to have as many as there are would be simply ridiculous. It just strikes me as lame to think that all these decendants are doing repeats of what their ancestors did over and over and over again.
I like to think of it as one very large overarching story, with the same core cast of Link, Zelda, and Ganondorf. There's still an element of repetitiveness, but at least here the core conflict is still identifiable between these characters. The games cover their lives as they travel through different eras of history.

Third, Link serves as a sort of anchor for the Zelda franchise. No matter what scenario or time the game is set in, Link is always Link. Because Zelda is a game where almost everything changes drastically from one game to another, it's important to have a constant character to keep the game grounded. (Think of Desmond from Lost trying to find Penny) This would be cheapened if the new Link was really just "Link's great great great great grandson who looks a lot like him".

As far as split timelines go, I'm a little more open to the idea of a second Link, but ultimately I still believe that there is only one. It would work one of two ways: Either the split timeline created a parallel Link, or Link just shifts from one timeline to another when he is reincarnated. I'm okay with either scenario here because there'd actually be an excuse for a second Link (Time Travel).

Finally, I have to address the Achille's Heel to my argument...FS and FSA.
Man am I the only person who wishes those games didn't exist theory-wise? It just blows everything else out of the water and forces a fantastic explanation. I could try to say that these 2 games exist in their own separate universe, but I believe a source from Nintendo has stated there is only one timeline. Quite frankly, I don't know enough about the plot of FS or FSA to explain the obvious discrepancy. Is there even a reason given why there's four Links? Probably not, but at the very least I can say that having four links also complicates the descendant theory. There's just no logical explanation for four of him to exist at one time, unless the current Link went to the past to get help or something. This is definitely the weakest aspect of a single Link theory, but I think because FS and FSA are so unique they cannot be used to confirm or deny the possibility of reincarnation.

 

[Locke]

First, to answer your question about the FSS, the four Links are actually the same person, split into four by the power of the Four Sword. This was stated in each of the three games. So you shouldn't have been so worried about that bit.

The rest, however....

Question: The beginning of the game talks about Link getting the green clothes and the passing down of the history, the hero dressed in green, etc. How many different Links are there? This doesn't seem like that was in Ocarina of Time, for example.

Eiji Aonuma: In our opinions, with the Legend of Zelda, every game has a new Link. A new hero named Link always rises to fight evil.

source

There are a myriad of different inconsistencies between the games that arise when looking at them from the perspective of there being one Link. The confirmed time periods between each game, WW-Link not being the HoT from WW's backstory (OoT), Zeldas being descendants of each other (see AoL, ST...), ....the list goes on; I can't even begin to scratch the surface, and I won't bother in light of the quote I produced above.

And to answer your point about Links being descendants of each other (I realize I'm going backwards), check out Demise's last line from SS:

Spoiler

Those like you... Those who share the
blood of the goddess and the spirit of
the hero... They are eternally bound to
this curse.
An incarnation of my hatred shall
ever follow your kind, dooming them to
wander a blood-soaked sea of darkness
for all time!

Demise confirms for us that Zeldas are in fact blood relatives of each other, while Links are only related in that they have the spirit of the hero (whether that means one distinct spirit, or just the quality of being courageous and heroic is a different debate). There is nothing in any game that suggests that Links have to be related. LttP-Link descended from the Hylian Knights, but that doesn't necessarily mean another Link. There are several non-Link Hylian Knights in OoT, for example. In fact, Link in WW is stated to not be related to the HoT. Each Link is a person who either just happens to be heroic or inherits the "spirit of the hero."

 

[kroni]

Thank you for the reply, Locke. I'm happy to know that FS and FSA won't be a problem. The above quote from Aonuma you cited does seem to go against it though. He says "a new hero named Link" which is hard to explain away. But then again, you're quote from Demise also shows that the curse is passed down through the "spirit" of the hero. He clearly distinguishes it from blood line because he also mentions the blood line of the goddess in the same sentence. This is significant because it shows that each "new Link" retains something that is referred to as a spirit. That sounds to me like a soul. It's possible that the Spirit of the Hero is more like a residual force left behind rather than it being each Link, but I don't see it that way. I can get on board with the idea that new Links and Zeldas may or may not come from the same blood line, as you have evidenced to me. But the spirit of the hero seems to be a frequent subject brought up in the games, and a new Link is born with the "soul" of the old Link whenever Ganondorf returns.
To sum all that up, I can't argue with your evidence but there are still plausible ways for only one true Link to exist, if you consider the soul to be Link rather than his body.

 

[GessieReppie]

TWW happens hundreds of years after OoT. I look forward to your theory about Link being frozen in carbonite during that period.

 

[DuckNoises]

Since the question has been answered, I'll be closing this thread.