Ocarina of Time
Their main goal in the video game is to rebuild Kakariko Village, but the boss is disgruntled by his employees for being so very lazy, just wandering around. He's also disappointed with his son Grog who just sits around all day. If the player visits the village at night, then Grog will explain that his parents, you, and everyone else in the world are disgusting. The player can converse with the other carpenters just by finding them, though by the looks of it their leader is right - they don't seem to be doing much work but rather are just wandering around.
Seven years later when Link as an adult returns to the village, everything is complete. The carpenters have moved out into Gerudo Valley, where they can be found inside of their tents. Their goal here is to rebuild the bridge that was destroyed sometime during the seven years Link was inside the Sacred Realm. Sadly, the only one of the carpenters that is left is the leader. The others have joined a band of Gerudo Thieves, leaving him to do the job all by himself. The Gerudos reject all of the carpenters, and lock them up throughout their hold. Link is required to free them and send them back to rebuild the bridge.
The carpenters return again in the Nintendo 64 title The Legend of Zelda: Majora's Mask. Here they can be found in Clock Town, and once more their leader is Mutoh (whose name was revealed in this title). Their role in this game is building the tower in which the people can observe the vast fireworks display which will ensue after a few days during a grand carnival.
During the third and final day, all of the carpenters except Mutoh have left the city. Mutoh looks up at the moon yelling at it, telling it to just come down already. According to him, all of his loved ones have also fled.
Oracle of Ages
In The Legend of Zelda: Oracle of Ages (note: they did not appear in The Legend of Zelda: Oracle of Seasons), the carpenters are planning to build a bridge to Symmetry Village. None of them excluding the leader are doing their jobs, though this will change when he has a talk with them.
In their most recent appearance in The Legend of Zelda: The Minish Cap, the Carpenters can be found throughout doing construction work and blocking certain parts of the worldmap so that Link cannot enter at the moment. If the player wishes he can fuse Kinstones with them.