Carpenter
The Carpenters Mutoh is the stubborn and short-tempered head carpenter of Hyrule. His young and Lazy employees are Shiro, Jiro, Ichiro, and Sabooru. They were introduced in Ocarina of Time, Mutoh leads his lazy employees sternly, but despite his best efforts, they never get much done.
As with many characters introduced in Ocarina of Time, they make many appearances throughout the Zelda series.
Ocarina of Time
During Link's childhood, Mutoh and his carpenters are working on a building in Kakariko Village on the orders of Impa, who hopes the village will someday be a "True City". The carpenters are lazy however, and Mutoh tries his best to whip them into shape. While hiding from Mutoh in order to avoid working, one of the carpenters tries to envision a job with little work and lots of pay. All that he can think of his his thievery, a career that he and his fellow carpenters will (attempt to) pursue seven years later. Mutoh's family seem to be some of the only current residents of the village, including his daughter Anju, and his son Grog. Mutoh is ashamed of his son for "sitting around all day", and is met with a similar reception as Grog calls Mutoh "disgusting". Anju refers to Grog as her brother,making Mutoh her father.
Seven years later, during Ganondorf's reign of Hyrule, the carpenters have departed from Kakariko Village after successfully completing only one building. They have now set up a tent in Gerudo Valley in order to restore the bridge that the Gerudo thieves have destroyed to ward off intruders. Mutoh however, is the only one remaining, as his carpenters have all abandoned him in a failed attempt to join the Gerudo thieves. The predominantly female bandits reject the lazy carpenters, instead holding them prisoner in seperate cells throughout their fortress. Once Link has rescued all four of the carpenters, the Gerudo acknowledge his strength and give him an honorary Gerudo Membership card, allowing him to roam the Fortress freely as a member of the Gerudo. After a scolding from Mutoh, the returned carpenters rebuild the bridge in Gerudo Valley.
Mutoh also holds a place in the trading sequence. After giving Mutoh the Poacher's Saw that his son Grog has left behind in the Lost Woods, Mutoh gives Link his Broken Goron Sword in return.
Majora's Mask
In Majora's Mask, Mutoh is a Terminian and the Head Carpenter of Clock Town and thus, is in charge of constructing the fireworks tower in the center of Clocktown. He seems to be extremely stubborn and is mostly always seen crossed-arm pose and laughing in a scoffing manner. Mutoh can be first found arguing with Captain Viscen in the mayor's office over whether or not to flee the town in the wake of the impending moon or to continue on with the carnival; both men trying to convince the uncertain mayor of their respective opinions. Should Link quell this feud with the Couple's Mask, Mutoh seems to disappear until the night of the final day, where he can be found at the foot of the completed fireworks tower (no other carpenters in sight) yelling spitefully at the moon "If you're gonna fall, then what's stoppin' ya, you monster?!"
Notably, he seems to have some sons who already fled the town and a wife, about whom he wonders of her whereabouts (whether she's fled or not) during the end of the meeting in the mayor's office. Also, he seems to dislike Kafei for going missing and compares him to his sons.
Oracle of Ages
They are once again slacking off in Oracle of Ages' prelude to Level 4, Skull Dungeon. Link finds the Foreman and he explains that his workers haven't shown up. Link has to search them out and lay down the law. The terrain will be different depending on whether he has Ricky, Moosh or Dimitri as his animal partner. After he puts them all back, Link is able to extend a bridge that leads to Symmetry City.
The Minish Cap
Mutoh's carpenters are the same as ever, but by fusing certain Kinstone pieces, they will construct various buildings all over Hyrule town. They also serve to block off areas developers didn't want Link to reach until a certain point. After finishing all their building jobs, they vanish.
Quote from The Legend of Zelda: The Minish Cap The Carpenters figurine:
"These carpenters may be rough around the edges, but they do good work. They may seem tough, but they're in touch with their femine side."