You are right in identifying Oedipus as the classic example of this statement. One of the reasons that this play is so famous is that Sophocles creates a situation where both the audience and quite a few of the characters know who committed the murder of the former king of Thebes but Oedipus, ironically the man who committed that murder, does not. What makes this irony more acute is the way in which he pledges himself to find that murderer and see him punished for the tragedy that has befallen Thebes. As the evidence stacks up against him, we see more and more how he is doing his best to ignore the truth, helped by characters such as Jocasta. However, note how he expresses himself when he is forced to truly know himself as the man who is the murderer he is looking for:
All come true, all burst to light!
O light--now let me look my last on you!
I stand revealed at last-
Cursed in my birth, cursed in my marriage,
Cursed in the lives I cut down with these hands.
Oedipus does his best to subconsciously ignore his true identity for most of the play, but when incontrovertible evidence forces him to see himself for who he is, he has no choice but to yield to the inevitable and finally accept self-knowledge. This is what makes him a perfect example who does everything he can to prevent knowing himself.