This is the watershed Q episode, where the character goes from menace to friend (so to speak). While he’s truly evil/heartless in the three Q episodes preceding this one, he’s actually on Picard’s side in the four that follow it.
TNG didn’t try humor as much as it should have, but it succeeded with this one brilliantly.
This episode also does high-falootin' well too:
Q: Don't be so hard on me, Jean-Luc. You've been a mortal all your life. You know all about dying. I've never given it a second thought. Or a first one, for that matter. I could have been killed. If it hadn't been for Data and that one brief delay he created, I would have been gone. No more me. And no one would have missed me, would they? Data may have sacrificed himself for me. Why?
PICARD: That is his special nature. He learned the lessons of humanity well.
Q: When I ask myself if I would have done the same for him, And I am forced to answer no, I feel, I feel ashamed.
PICARD: Q, I'm not your father confessor. You will receive no absolution from me. You have brought nothing but pain and suffering to this crew. And I'm still not entirely convinced that all this isn't your latest attempt at a puerile joke.
Q: It is a joke. A joke on me. The joke of the universe. The king who would be man. As I learn more and more what it is to be human, I am more and more convinced that I would never make a good one. I don't have what it takes. Without my powers, I'm frightened of everything. I'm a coward, and I'm miserable, and I can't go on this way.
Deja Q is also the origin of the Internet face-palm meme: