In "Lord of the Flies", which boys were the most successful leaders? For those who were poor leaders, what factors caused them to struggle?

Defining "successful leadership" is a task all of its own; Jack and Ralph were both successful leaders, but in very different ways. A good generalization would involve establishing the goals for a group, and/or the means of achieving those goals, and then actually achieving them. A less goal-oriented but no less powerful definition would involve simply the appearance or social status associated with leadership, in the form of social dominance such as being able to...

Defining "successful leadership" is a task all of its own; Jack and Ralph were both successful leaders, but in very different ways. A good generalization would involve establishing the goals for a group, and/or the means of achieving those goals, and then actually achieving them. A less goal-oriented but no less powerful definition would involve simply the appearance or social status associated with leadership, in the form of social dominance such as being able to direct and control conversations, represent the interests of others, and hold responsibility for critical tasks. 

Jack and Ralph are clear candidates for successful leaders by any of the definitions above, but Jack is definitely the more successful of the two; were it not for the intervention of the naval captain, Ralph probably would have died, and this pretty much disqualifies him as "successful". Ralph was a successful leader at the outset of the story because he was able to rely on the inherent restraint that the boys had learned via "civilized" influences, but his leadership was ultimately more of a title and posture than a practice; he was unable to actually get others to do what he wanted on a consistent basis.

Piggy and Simon are good candidates for "failed" leadership. Piggy was clearly the most intellectual of the boys, but the combination of his awful social skills and the boys' immaturity ensured that Piggy could not be appreciated for his more abstract qualities; it didn't help that he aggravated his own ostracism by failing to take social cues or improve himself in that regard. Instead, he often doubled-down on his insistence that he was right; this culminates in his statement about his glasses, that giving them back is "the right thing to do"; in Piggy's mind, morality is not abstract or relative, and his attempts to enforce this on others without the power to back it up simply make him look foolish.

Simon could have been a leader because he was an intellectual counterpart to Piggy, but a less obstinate one; he was a more humble and reasonable voice, but his timid nature prevented him from asserting himself in the face of the mockery the other boys threw at him for his difficulty in public speaking. Simon is often compared to the "prophet" archetype, and it should come as no surprise that young boys would be unable to appreciate or respect the concept of prophecy or foresight. Like Ralph and Piggy, Simon's greatest problem was the fact that his better qualities were not sufficiently developed, and those around him could not appreciate them for their own sake.