In Majora's Mask, the Hero's Sword is in Link's posssession from the very beginning of the game. Thus, it is presumed to be the Kokiri Sword found in Ocarina of Time. It is the weakest sword in the game, but can be upgraded at the Mountain Smithy at Snowhead to the Razor Sword, and then to the Gilded Sword.
The Wind Waker
Link gains the Hero's Sword on Outset Island after clearing Orca's sword training. Furthermore, Link walks up to the nearby forest to save Tetra. Tetra's friends, the pirates, come up to see if she is all right. Link and the pirates walk out of the forest and see that Aryll has went up to see her brother. The Helmaroc King then comes flying towards Aryll and grabs her by its claws, and takes her to the Forsaken Fortress. After that had occurred, Link climbs aboard the Pirate Ship and travels to said Fortress. The pirates launch Link to the Forsaken Fortress, but he loses the Hero's Sword on impact. He manages to make it through the area without his sword and without being harmed. Later, he finds the Hero's Sword and enters the prison where Aryll is hidden. He then proceeds to try and save her, but the Helmaroc King grabs Link and takes him to Ganondorf. Afterwards, he disposes Link by throwing him into the ocean. Eventually, the Hero's Sword is replaced by the Master Sword.