Top dog Athenian playwright, Sophocles, gets the award for most well known version of the story of Oedipus. His ridiculously famous play, Oedipus the King, is often said to be the best example of ancient Athenian tragedy, and it's still performed all the time around the world.
It seems like Sophocles just couldn't get enough Oedipus, because he also wrote Oedipus at Colonus, which tells of Oedipus's death, and Antigone, which tells the tragic fate of his children. Together these three plays are often called Sophocles' Oedipus or Theban Plays.
Don't go thinking that Sophocles was the only guy to ever write about Oedipus, though. The granddaddy of all Greek playwrights, Aeschylus, wrote a trilogy of plays chronicling the woes of Oedipus and family. Unfortunately, the only play that's still around is Seven Against Thebes, which tells the story of Oedipus's sons Eteocles and Polyneices duking it out over the throne after their dad is already dead. The plays starring Oedipus have unfortunately been lost to the sands of time. (Oooh, poetic.)
Euripides, the main rival of Sophocles, also wrote his own version of the Oedipus story. Only bits and pieces of his version remain, but scholars say it was different in a lot of ways from Sophocles' take. This is totally clear because Oedipus does make an appearance in Euripides' Phoenician Women, which definitely goes a different way with several key plot points.
These playwrights weren't the only ones to take on the story of Oedipus either. Other big deal writers like Homer, Ovid, and Seneca the Younger all gave the most unlucky guy of all a little bit of their time. These days, Oedipus is also known for inspiring Sigmund Freud's concept of the "Oedipus Complex." This theory is often over simplified as meaning that every guy secretly wants to kill their dad and sleep with their mother just like Oedipus, but it's really a lot more subtle and complicated than that. Click here for a little more detail.