In the Legend of Zelda games we have a constant set of characters, that act and perform very similarly from game to game, yet with a few differences.
How are these characters (Link, Zelda and Ganondorf) connected through the series?
I found this on Wikipedia:
The protagonist in each game is usually not the same incarnation of Link, but a few exceptions do exist.
And various discussions, but I'm after an answer from canon as far as that is possible.
The short answer is: Ganon/Ganondorf is always an incarnation of "Ganon" so whether that counts as him being the same person or not, is up to your personal definition. Link however, is rarely the same person, and is always given the name Link for consistency. He is generally a different "chosen one" style boy hero, with no claim to fame at the time of the adventure's onset. There are some exceptions.
The Long Answer is:
To understand the various Links and Ganondorfs/Ganons you first have to understand the timeline:
Official Timeline
According to the official timeline, the various Links are separated by often hundreds of years, and are often the same age at the time of choosing. This very simply shows that the Links and Ganon's are not the same physical people.
Now, while that may seem unrelated... the fact is that in Ganon's case, he is "sort of" the same guy all the time. By sort-of, I mean he is not the same physical body, but always some kind of reincarnation of Ganon. Where this gets foggy is that the leader of the Gerudo is always said to be this reincarnation of Ganon. So, he is kinda the same guy, but through various rebirths/awakenings.
Link, however, is sometimes the same hero, sometimes not. The Link of OOT and Majora's Mask are the same link. But, the Link for Zelda 1 and Link to the Past are different. It is actually rare for Link to be the same person.
In Wind Waker it is mentioned that "Link" the boy hero, is always chosen during a time of peril within an era.
Having said, that, games that take place during the same era can sometimes use the same Link. Note that most of the games start out with Link having no Hero status, often having no sword at all. This is not the case in Majora's Mask, as Link IS a hero at the time, but is stripped of all his equipment and transformed into a Deku before the adventure begins.
It's irrelevant who the Link of Link's awakening is, the events within it don't actually happen.
The Resurrection Theory
It has been made fairly clear that the spirit of Ganon has been resurrected throughout the various timelines as recurring spirit of hatred, he often has very different backgrounds. The one common bar is that Ganondorf / Ganon is of the same spirit.
The less clear item is that Zelda and Link may also be reincarnations of one another. This is hinted at, but never clearly defined. The goddess chooses a hero for the ages and often imbues him with the Master Sword (which is said to always be the same Master Sword, btw). Regardless, there is a continual cycle of Ganon's hatred casting his anger over the land, and a Hero of Time taking up the will of the goddess to strike him down.
The example furthest up the canon is of course Skyward Sword. Watching the ending sequence will explain the whole cyclic Ganon/Link/Zelda thing.... but is a huge spoiler.
Different Links
Zelda I and Zelda II (same Link, different Zelda)
Zelda, Link to the Past (possibly same Zelda as Zelda II, but different Link)
Oracle of Seasons, Oracle of Ages, Link's Awakening (same Link in all 3)
Ocarina of Time and Majora's Mask (only one has Ganondorf or Zelda, same Link)
Wind Waker and Phantom Hourglass
Twilight Princess (This is an alternate timeline from WW and PH. So, I consider it to be a different Link as no one Link experiences WW, PH, and TP events.)
Skyward Sword (the earliest piece of the timeline, the Zelda in this one is said to be the original Zelda, predating the Zelda of Zelda II and Link to the Past).
Minnish Cap (this is a strange part of the timeline, but it's clear you're no hero at the onset of this one.)
