When Simon is hallucinating and supposedly talking to the pig's head, the head says that he (the evil) is inside of man and that is why they will never be able to eradicate it. Simon is the first to realize this when he says to the boys, "Maybe the beast is us." However, he loses sight of this perception and runs down the hill to tell the boys that the "beast" is only a dead parachutist. He, of course, is killed because he is mistaken for the "beast" during a ritualistic dance. Even after Simon is dead, the evil continues to be part of the boys and eventually, Piggy is killed and the boys almost succeed in killing Ralph. The reason the evil continues is that it is innately part of the boys. There is no strong government or leadership to control it and so it is left to take its natural course, as the pig's head or "Lord of the Flies" predicted.
The "Lord of the Flies" "propecy is shown when Simon is hallucinating and talks to the lord if the flies. While he talks to it, it tells him "or else we shall do you? See? Jack and Roger and Maurice and Robert and Bill and Piggy and Ralph. Do you. See?."
Meaning that all those people he just named will partake in Simon's death. Which, they did in chapter 9 during the ritual they thought he was the "Beast".
Simon did not see that all those named were already uncivilized and doing rituals. He thought that they still have some order and discipline within themselves.
Two of Simon's prophecies are fulfilled. The first is, as ms-mcgregor points out, is that "the beast is us", but he also makes a second.
When the boys are on the other side of the island, Simon tells Ralph 'I just think you'll get back all right'. This, of course comes true at the end of the novel, meaning that Simon was right about Ralph.
It shows possibly even more foresight that Ralph uses the pronoun 'You', rather than 'We'. suggesting that he possibly knows he will no get home.