Case Description: Complainant (the People of Thebes) accuse Defendant (King Oedipus) of murder and incest. When Thebes was infested by a terrible plague, King Oedipus sent his brother-in-law, Creon, to go ask the Oracle what the deal was. The Oracle said the plague had been sent by the gods, because Thebes harbored the murderer of Laius, the former king. Being the good king that he was, Oedipus set out to solve the mystery. He eventually figured out that he had killed Laius in a fight on a road awhile back, not knowing who he was. During his investigation, Oedipus also finally figured out that Laius was his real father, and that Jocasta, who he'd fathered four kids with, was really his mother. Oops.
Case Status: Case closed. As punishment for his accidental crimes (or maybe just because he was depressed), Oedipus gouged out his own eyes. He then exiled himself from Thebes to wander blindly through the wilderness with only his daughter, Antigone, to guide him.
Addendum: In some versions of the story, Oedipus is forced into exile by Creon.