From Zelda Legends Wiki
Link is the hero and main playable character of all the Zelda games. Although he is the main character, there is actually not that much known about him. This is mainly due to the fact that in all games you are rarely aware of what he says, so you never get to hear much about his personality and such things. The main trademarks of Link's appearance are his pointy ears that all Hylians share and his green clothes, including his trademark pointy green cap and his trusty sword & shield.
The Legend of Zelda
A Link to the Past
Ocarina of Time
Link in OoT, the Hero of Time, is perhaps the most well-known and revered hero in Hylian history.
At first thought to be a little Kokiri from the forest, Link is the son of a proud Hylian mother. After the Great Deku Tree passes on, Link is given a task to perform: find the Princess of Destiny, Princess Zelda. The princess tells him to get two of the Spiritual Stones (he already had the Spiritual Stone of Forest entrsuted to him by the Deku Tree), passed down the Gorons, and the Zoras and use them with the Ocarina of Time to protect the Triforce, or, to be strictly accurate, obtain the Triforce before Ganondorf, who came to Hyrule to get it.
But this plan backfires when Zelda is chased from her castle by Ganondorf to go into hiding. She entrusts Link with the Ocarina, so he can open the Door of Time, the barrier that protects the Triforce, inside the Temple of Time himself to obtain the Triforce. However, behind the door was not the entrance of the Sacred Realm (the resting place of the Triforce) itself, but a final safeguard for protecting it. This safeguard was the Master Sword, the Sword of Evil's Bane. Only a person deserving of the title of "Hero of Time" could pull it from the Pedestal of Time.
At the moment Link lifts the sword from the pedestal, his spirit is sealed inside the Temple of Light, the temple where the Triforce rests, leaving open the entrance to it, so Ganondorf is able toget it.
Link is locked in sleep for seven years until Rauru, the Sage of Light awakens him, telling him that because Ganondorf obtained the Triforce and became tyrant of Hyrule, Link, with the Master Sword, must be the prophesied Hero of Time, the only one able to awaken the rest of the Sages, so they can seal the Evil King inside the Evil Realm that the resting place of the Triforce has become.
After Link awakens all the Six Sages, he finds Princess Zelda.
Or rather, she finds him, since she was watching him the whole time in the guise of a male Sheikah warrior, Sheikand now revealed herself to be Zelda, as well as revealing that Ganondorf had only got the Triforce of Power, and telling him he's the holder of the Triforce of Courage, and she the holder of the Triforce of Wisdom and the Seventh Sage. At the end, Using the power of the Seven Sages, they are able to seal the Evil King inside the Evil Realm.
The Link in Majora's Mask is generally accepted to be the same Link from Ocarina of Time.
This, of course, is only partly true.
The Majora's Mask Link has in his possession a metalic shield, and can use it as Young Link could the Deku Shield in Ocarina of Time.
This suggests that after Zelda sent Link back into his childhood for the last time, Link asked Zelda (or Zelda vollentered to) make a specialized shield made of metal for him; one that he could use like the Deku Shield.
This is consistant with the diffirent design on the shield, dispite the same graphic format.
Also, in Majora's Mask, Link makes a very distinct grunt when he jumps, as well as jumping in the way of frontflips and summersaults - in Ocarina of Time, Link did neither, either as a Child or an Adult.
This suggests that the Majora's Mask Link is in fact older and more experianced then the Young Link of Ocarina of Time
(note: all suggestions a theoretical)
Oracle of Seasons/Ages
The Wind Waker
Four Swords Adventures