Very interesting giveaway. I wish to take part in it as well, count me in for Edna & Harvey - The Breakout. I have the sequel, but not the original. Kind of a messy situation to be in. I'm holding off on playing the series for now, so this chance proves to be very tempting. As for the discussion at hand:
"What makes a Point & Click Adventure work for you?"
Hard to say as I have very limited experience with point & click games and more experience with P&C - Visual Novel hybrids. In both cases I think the game has to be mysterious in order to captivate me. If it's not entertaining in the sense that it at least makes me chuckle, like the Monkey Island games do, I'm expecting a good story with a lot of mystery.
"Is it the puzzles, the story?"
A combination of both. I enjoy a good story, but it goes beyond certainty that the mental challenge of puzzles is an alluring element.
"Which have you found worked well for you, and which failed in your opinion?"
Hard to say: Walking Dead was especially great. While not much of a point & click game, the story just sucked me in and I played that game for a straight 14 hours and finished it the next day I got it. But point and clicks like Monkey Island worked flawlessly with me, even in spite of really obscure puzzles. These are sadly the only 2 examples coming to mind, though I'm sure I've played more point and clicks besides that.
"What are your favorite P&C's?"
I already mentioned them, so I feel at this point it would be too repetitive to mention them again. :P Sadly only the most memorable of them stuck with me, or these that I have played and completed. Syberia is an honorable mention though. The gorgeous visuals and engaging story are what makes that game series a must play.