The most important prophecy in Oedipus Rex by Sophocles is one that was made before the actual action of the play. The oracle at Delphi prophesied that if Laius had a son, the son would kill him. Thus, when Oedipus was born, Laius ordered him killed. The servant ordered to expose Oedipus (the traditional Greek manner of letting unwanted infants die without bringing down the pollution of murder) gave the infant to a shepherd rather than killing him. The child Oedipus ended up being adopted and raised by the childless King Polybus, and Queen Merope of Corinth.
When Oedipus meets Laius at the crossroads, Laius does not know that Oedipus is his son and Oedipus does not know Laius is his father. When Laius and Oedipus fight and Laius dies at Oedipus' hands at the crossroads, the prophecy is fulfilled.