What is the role of fate in Oedipus Rex?

To add to the superb answer above...

Fate all too often seems like some nebulous catch-all.  An excuse.  A scapegoat.  Something unforeseen.  Dramatic irony.  All this commentary about "fate catching up with Oedipus," I think, is pandering nonsense.

Fate in Oedipus cannot be confused with punishment or suffering.  Fate is not the Sphinx, or the plague, or suicide, or exile.  This kind of analogy-making is non sequitir, faulty logic.  To permit this is to negate humankind's responsibility and ability to rise above suffering.  To place so much emphasis on fate diminishes the play as a whole.  Fate renders the play deterministic, not a thoughtful craft at all.

Fate is only what Oedipus is thrown into, as it is with all of us: our family, our gender, our blood--that which is completely out of our control.  Obviously, we cannot choose who are our parents, or what genetic abilities or handicaps they have passed on to us.  For Oedipus, it was his crippled leg.  He had no choice in being crippled.

The only fate sealed in the Oedipus trilogy comes when his parents decide to cut his angles and leave him for dead.  This is the dark secret that sets tragedy in motion.  The rest, in my opinion, is a series of choices: some good, most bad.  I don't think it was fate that Oedipus killed his father or married his mother or brought the plague to Thebes or caused Jocasta to suicide or blinded or exiled himself.  These were all choices he made, not the results of fate or oracles or the gods.  Nothing is working behind the scenes--only Sophocles!

Yet, in the end, Oedipus takes responsibility for each of his  choices.  He suffers with dignity.  He does not suicide, like Jocasta.  In the end, he has a kind of victory over these choices, as he is given a sacred burial.  Camus calls him a hero for this.

But, in the end, after Oedipus dies, his family continues to succumb to suffering and death.  Were they destined to suffer?  Of course not.  Did they suffer from hubris?  Of course.  Is hubris the same as fate?  Of course not.  Is hubris the result of bad choices and decision-making?  Of course.

In other words, fate is only that which is completely and utterly out of Oedipus' control.  It is his gender, the color of his skin, hair, and eyes.  It's family secrets, an inscrutable past.  In particular, it's that crippled leg.  I can't think of any other instance of fate that is any more crucial to the plot of this play.