Kaepora Gaebora

Kaepora Gaebora (ケポラ・ゲボラ, Kepora Gebora) is an owl introduced in Ocarina of Time. He is both very large and very knowledged, traits he uses to carry the Hero places and to advice him on the next course of his quest.

In Ocarina of Time, Kaepora Gaebora is said by a Gossip Stone to be the reincarnation of an ancient sage. It is therefore not unlikely his Ocarina of Time and Four Swords Adventures incarnations are the same character. It also helps explain why he knows so much about Hyrule and why he keeps track of Link's proceedings.

Ocarina of Time
Kaepora Gaebora awaited Link when he left Kokiri Forest, giving him encouragements on the quest the Great Deku Tree had put him on and directing him to Hyrule Castle. He then left with the message they'd meet again.

True to his word, Kaepora Gaebora was often around when Link entered or was near a new area to offer information. On two occasions he even provided easy travel by flying Link back to a more central area. After Link awakened in the future however, Kaepora Gaebora was nowhere to be found, with one exception. When Link learnt the Requiem of Spirit from Sheik, Kaepora Gaebora looked on, but did not make his presence known.

Oddly, he seems to refer to this moment back in the past years which Link had to travel to to obtain the Silver Gauntlets. That also was the last time the two spoke, as Kaepora Gaebora noted that he was no longer necessary. With one last piece of advice on the battle with Twinrova ahead, he flew off not to return again.

Majora's Mask
In the alternate dimension of Termina, the wise owl too has a counterpart. He taught Link the Song of Soaring, which allowed Link to warp to different activated owl statues. He is seen again at Snowhead, where he tells Link where the Lens of Truth is and helps him get to the cave where it is placed by using his feathers to point to a group of invisible platforms that Link can use to reach the cave.

Four Swords Adventures
Kaepora Gaebora himself makes a reappearance in Four Swords Adventures, serving much the same role he did in Ocarina of Time.

Theories
Sage identity - Being said to be the reincarnation of an ancient Sage, Kaepora Gaebora is subject to much speculation on his original identity. It is often argued that Kaepora Gaebora is Rauru's form outside of the Sacred Realm. This assumption is based on two things mainly. For one on that they both are/have been ancient Sages, and furthermore on that one of the Gossip Stones' states that "[Kaepora Gaebora's] character is rather lighthearted", which is thought to be a reference to Rauru's status as the Sage of Light. However, a lot of the things said by Rauru and Kaepora Gaebora don't add up if they are supposed to be the same character, like that Kaepora Gaebora did not believe in "the tales of a boy who could travel back and forth through time", whereas Rauru was the very person who caused that time travel. Or that Kaepora Gaebora on his last appearance notes that it's his "last advice", whereas Rauru goes on guiding Link for a little longer. While it may be theorized Rauru didn't want his alternate identity from being discovered, there is no reason whý he wouldn't want that.

Another popular suggestion is that Kaepora Gaebora is the reincarnation of Kasuto - a theoretical Sage assumed to exist due to Ocarina of Time ' s system of naming its Sages after towns from The Adventure of Link.

Trivia
Owls are a common theme throughout the The Legend of Zelda, usually, indeed, in relation to the gaining of knowledge. If and how there is a connection with Kaepora Gaebora is largely unknown.
 * In Link's Awakening, there is an owl character who guides Link with words of wisdom. Since both Kaepora Gaebora and this owl are owls who give Link directions, it is possible that the owl from Link's Awakening may have inspired the later Kaepora Gaebora. From an in-universe perspective, it is possible that the two's likeness is to be explained the other way around. Since all characters from Koholint are a product of either Link's or the Wind Fish's minds, in some cases obviously inspired by someone they know, possibly the memory of Kaepora Gaebora created the owl.
 * Eldin, the Light Spirit of the Eldin Province in Twilight Princess, is also an owl or perhaps another kind of a large bird.
 * Owl Statues appear in Link's Awakening, even moreso in its DX version Oracle of Ages, Oracle of Seasons and Twilight Princess. They serve to hand out information and hints on nearby challenges.