In The Hobbit, there are two important turning points to consider: first, in the development of Bilbo as a character but also in terms of the expedition of the dwarves to reclaim the Lonely Mountain. Bilbo's turning point as a character occurs in Chapter Eight when he successfully vanquishes the spiders and rescues the dwarves. In this moment, Bilbo not only gains a much needed sense of self-confidence, but also the realization (and appreciation from the dwarves) that he has proven himself a valuable member of the company.
The second major turning point of the story, and the true climax of the novel, deals with the original purpose of the dwarves' journey and occurs in chapter 17 during the Battle of the Five Armies. In this moment of the story, the outcome of the adventure hangs in the balance--the dwarves could win and regain control of the Lonely Mountain or the orcs and goblins could be victorious and probably kill all of the heroes, leaving the reader with a much sadder ending to the tale. Fortunately, in this turning point, the dwarves gain some much needed assistance at the very end of the battle in the form of the giant Eagles and Beorn, who kills the goblin king, thus ensuring victory for the dwarves.