Matsya Avataar and Boat
The very first reference of boat is of Bhagavaan's Vishnu Himself. Bhagavaan's 2nd Main Avataar or 11th of all Avataar is Matsya Avataar - the Fish Incarnation. In this Avataar the boat is prominent. After Brahmaa's a day (a span of 4320 million human years) is over, the whole Prithvi is covered with water. After the day is over Brahmaa Jee goes to sleep. As he goes to sleep, all Creation dissolves into his sleep, signifying the end of Creation, except the Ved as they are immutable or beyond destruction. Their habitat is inside Brahmaa. They contain the instructions for Creation, and are hence indispensable to resume the Divine Creational Process when Brahmaa Jee awakes next day.

Bhaagvat Puraan, reports, that once Brahmaa Jee yawned accidentally and the Ved came out of his mouth. Meanwhile, Hayagreev Daitya in making efforts to gain immortality, a prerogative of the Devtaa, was wandering nearby. He instantly stole the Ved and devoured them. This precipitated a crisis. Vishnu saw the entire event so He started thinking on how to retrieve the Ved. He located the pious King Satyavrat, offering prayers to Vishnu. He immediately assumed the shape of a tiny fish and swam into Satyavrat's hands. Seeing that that fish he tried to return it to the river, but that fish requested him to save it from being eaten by big fish in the river. The kind King brought the fish home and put it inside a vessel, full of water. Overnight, the fish outgrew on a surprising scale. Manu had to shift him from the vessel into a bigger tank. But the fish continued growing abnormally. It requested Manu for a larger space to live, and Manu accordingly kept it in a pond, then transferring it in a large lake and then he brought it to sea. But the fish urged the King not to leave him in the ocean otherwise, the gigantic ocean-beings would swallow him. The king Satyavrat, amazed by the extraordinary growth-speed of the magical fish, requested it to disclose its actual identity.

Vishnu made His identity and purpose of assuming the form of fish. He warned him about the forthcoming Pralaya or the Great Deluge - "I have manifested for the protection of this universe and for the destruction of the wicked. Just a week from now, the ocean will rise and inundate the entire Universe. At that time you will see a spacious boat approaching you. Do collect all the seeds , plants and animals required for the next spell of creation in the meantime and get into the boat and wait for me. Make Vaasuki Naag as the rope to tie it in my one horn. Sapt Rishi will also be with you." After having instructed like this the fish disappeared. As had been predicted by the Divine Fish, a flood came on the 7th day and the whole Earth was covered with water. Meanwhile, a boat appeared and the King Satyavrat boarded the boat with the seeds, plants and animals, and the Sapt Rishi, to take refuge in the boat. When everybody had boarded the boat, a fish with a horn appeared on the scene and the boat was fastened to the fish's horn with Vaasuki Naag as rope. They sailed in the turbulent water through Brahmaa's whole night.

Nishaad's Boat in Raamaayan
The second reference we find of Guha Nishaad who took Raam, Lakshman and Seetaa across the Sarayoo River when they were exiled by their father Raajaa Dasharath. Tulasee Daaas Jee has described this incident very beautifully in his Maanas - "When Raam requests Nishaad to take them across the Sarayoo River, Nishaad remembers Ahalyaa's incident and says politely - "First permit me to wash your feet, lest the dust of your feet turn my boat into a woman. I am a poor man, this is the only means of my livelihood. If it is gone how will I feed my family? And then from where I will maintain another woman too." Raam smiles and permits him to wash His feet. Nishaad takes them across Ganagaa River and Raam gives him Seetaa's ring as his fee, he politely refuses to accept it and says - "As I have taken you across Gangaa, when my turn comes, you also take me across this world, that will be my fee."

Satyavatee's Boat in Mahaabhaarat
(1) Daash Raaj's daughter Satyavatee also had a boat in Mahaabhaarat and she used to carry passenger across Yamunaa. This boat was a very important boat in turning the events in Mahaabhaarat times. The first time this boat became the means of meeting place of Satyavatee and Rishi Paraashar (grandson of Maharshi Vashishth). Paraashar was crossing Yamunaa River in Satyavatee's boat that he got attracted to Satyavatee and asked her to surrender to him. When Satyavatee told that she was scared of the society as she was a maiden, he created a mist around them both and had her. As a consequence she gave birth to Ved Vyaas Jee who fathered Raajaa Shaantanu's son Vichitraveerya's widows' sons - Dhritraashtra, Paandu and Vidur (by the widow's trick). This surrender gave her the ability to attract people to her by her fragrance which spread one Yojan around - this was sage Paraashar's blessing and thus she came to be known as Yojan-gandhaa.

(2) Next time, because of this fragrance, Hastinaapur King Shaantanu got attracted to her and when he saw her, he got lost in her beauty. He wanted to marry her but Daash Raaj put a condition that he would marry Satyavatee to whom only who will give her children the kingdom. Unfortunately by then Shaantanu had already declared Gangaa's son Devadatt his heir. He could not do injustice with his first-born son, so he could not agree with Daash Raaj. As he was love stricken with Satyavatee's love, he became very sad. Devadatt noticed this and found out the reason of this sadness. As he knew it, he went to Daash Raaj's house and took a vow not to claim the kingdom for his whole life and requested him to marry Satyavatee to his father. But Daash Raaj was still satisfied, he said - "If your children asked for the kingdom then...?" At this Devavrat took another vow not to marry his whole life. Since that day he came to be known as Bheeshm. After this vow Daash Raaj married his daughter Satyavatee to King Shaantanu.

Vidur's Boat in Mahaabhaarat
Another time Vidur Jee provided a boat for Paandav to escape from Laakshaa Grih fire event. As they came out of the tunnel there was the River Gangaa which was to be crossed. A boatman sent by Vidur, was ready there to take them across the river. he took them across the river and dropped them there. From there they started their journey in secrecy.

Noah's Arc
This example is not from Hindu scriptures, it is from Christianity and Bible, but it is very famous. Noah built a vessel in the Genesis flood narrative (Genesis 6-9), by which he saves himself, his family and a remnant of all the world's animals when God decides to destroy the world because of its evil deeds. God gives Noah detailed instructions for building this ark: it is to be made of gopher wood, smeared inside and out with pitch, with three decks and internal compartments; it will be 300 cubits (1 cubit = 18") long, 50 cubits wide, and 30 cubits high. It will have a roof "finished to a cubit upward", and an entrance on the side.