Bilbo and Thorin

Overview
Bilbo and Thorin initially got off the wrong foot, meeting in Bag End. Thorin openly mistrusted Bilbo and didn't believe Bilbo was a valuable asset to the company, but Bilbo was unaware of Thorin's desire to not look out for him during their journey. After learning the tragic backstory of how Thorin lost his family and his homeland, Bilbo found a new form of respect for Thorin but they remained at odds with each other. He rescued Bilbo at least twice: once by not risking Bilbo's life when the Trolls held him hostage and a second time when Bilbo nearly fell off of the cliff. Despite Thorin's mistreatment of him earlier, Bilbo saves Thorin's life once when battling Azog's warrior. In gratitude for Bilbo saving him, Thorin's view of Bilbo changed: instead, a person who can defend themselves, and what Thorin asked for: loyalty, honor and a willing heart. He apologizes that he was wrong about Bilbo and literally and physically embraces him, something that shocks Bilbo, who quickly forgives Thorin and returns the favor.

Their friendship continues throughout the trilogy, close to the point where Thorin lets Bilbo goes on his own and scouting for Azog the Defiler and most of the time, Bilbo saved Thorin and the other dwarves. At this point, Bilbo respects Thorin, and vice versa. Bilbo defends Thorin against the Men of Lake-town and has regarded him as a friend. Later on, Smaug tried to take away Bilbo's friendship with Thorin by lying to him, claiming that the dwarf was using him and found his fate worth nothing, but the hobbit refused to believe him and was also worried that Thorin would fall to the same gold sickness his grandfather suffered.

Trivia

 * Bilbo's and Thorin's relationship mirrors Frodo and Sam's relationship, as well as Gandalf and Pippin's in Lord of the Rings
 * Martin Freeman jokingly stated in an interview that he never judged Bilbo's sexuality and said, "For all you know, he could be in Love with Thorin."