For me, one of the most admirable traits that Oedipus reveals is after he has blinded himself and when he returns to the stage and seems to accept his fate and his identity without seeking to lay the blame anywhere else. Notice what he says in this crucial speech:
What grief can crown this grief?
It's mine alone, my destiny--I am Oedipus!
In particular, the final line is very important as he comes to own his own destiny and what has happened to him, and to declare who he is and how his destiny and fate is linked with his identity. This acceptance of such tragedy is actually incredibly admirable for a character who, at this point in the play, has lost everything and has just plucked out his own eyes. It helps us to have respect for him. Even though he was perhaps too arrogant at the beginning of the play as he casts himself as the father of Thebes, the way he faces up to and accepts his problems and fate here shows that he is worthy of great respect and sympathy.