Hokage

The are the leaders of Konohagakure. They are generally acknowledged as the strongest in the village, although ideology and renown plays a large part in their being chosen for the position. Four shinobi and one kunoichi have gained this title so far, with another shinobi gaining the title of Hokage Candidate.

Overview
Generally, the new Hokage is selected by the current Hokage upon their retirement, but if the old Hokage dies or is incapacitated before being able to do so, the Fire Daimyō will appoint a Hokage Candidate upon the recommendation of the Konoha council and the Fire Daimyō council. Afterwards, the candidate will need to be approved by the jōnin of the village to become officially Hokage.

After being approved, they move into the Hokage Residence to live in and have their faces carved out in the monument behind it. If the former Hokage is still alive, they will generally keep helping out, making the transition easier and more stable. The Hokage carry their title for life, even after retiring from active duty. The Hokage's office is located in the administrative section of the Academy.

Alternate Fourth Hokage
In the Genjutsu World in Naruto 6: Road to Ninja, Kizashi Haruno was the Fourth Hokage, however, like Minato in the real world, he died protecting the village.

Temporary Hokage
Naruto Uzumaki was made Hokage for a week in the storyline of Naruto: Ultimate Ninja 3.

Trivia

 * All of the former Hokage have been sealed away in the stomach of the Death God summoning. Kabuto Yakushi notes that none of them can be reincarnated via the Summoning: Impure World Reincarnation technique. All four, however, were eventually freed by Orochimaru from the Shinigami's stomach, and reincarnated by him.
 * All Hokage have had some connection to each other: the First and Second were brothers, the Third was the student of the Second and First, the Fourth was the student of Jiraiya, who was a student of the Third, and the Fifth is the granddaughter of the First, the grandniece of the Second, and the student of the Third. Jiraiya, a fellow Sannin and student of the Third, was also nominated for the title of the Fifth, but turned it down. When Kakashi was considered for the position of the Sixth, his connections as the Fourth Hokage's student almost cemented his selection. The former acting Hokage, Danzō, was once a rival for the position as Third Hokage, and disagreed with the peaceful ideologies of the five Hokage although he was once Hiruzen's close friend and fought under the Second Hokage during the First Shinobi World War.
 * At least three of the Hokage are known descendants of the Senju clan.
 * At least four of the Hokage had their official office photographs taken while wearing a ceremonial necklace of sorts.
 * Hiruzen Sarutobi, the Third Hokage, was said to be the strongest Hokage in the village's history, as well as strongest of the Five Kage of his era.
 * Kakashi Hatake has been considered a prime candidate for the position as Hokage by several characters.  He would have been officially appointed as the Sixth Hokage if Tsunade hadn't woken up moments before hand.
 * According to Asuma Sarutobi, his student Shikamaru Nara has the ability to become Hokage, but won't due to him being too lazy to want to.
 * Samui heard several villagers stating that they considered Naruto worthy of becoming Hokage after his defeat of Pain.
 * Orochimaru was once a prime candidate to be the Fourth Hokage, but due to his lust for power and lack of love for the village, the Third passed him over.
 * After Orochimaru was passed over for this position, Hiruzen intended to choose Jiraiya to be the Fourth Hokage, but Jiraiya refused due to his journeys as an author and his quest to chase down the renegade Orochimaru. After Hiruzen and Minato died, Jiraiya was once again offered the position as the Fifth, but he once again rejected it. When Tsunade went into a coma, the Fire Daimyō commented how he would have liked Jiraiya to be the Sixth, but by that time Jiraiya had already died.
 * Hashirama Senju is the one who created the term Hokage, and upon creation, wanted Madara Uchiha to be the First Hokage.