I would like to propose a badge to recognize users that ask good questions that are hard to answer. My proposed criteria for the badge(s) would be along the lines of:
Bronze: [no bronze along these lines]
Silver: [stumping] or [bewildering] ask a question that receives a score of 10 before getting an answer and is unanswered for at least 3 days.
Gold: [perplexer] ask a question that receives a score of 25 before getting an answer and is unanswered for at least 7 days.
Of course some sites will award this more than other but, okay. I further would like to stipulate that deleted answers should not count as spammers could kill an opportunity to gain this badge with the old "jhgdashjgadsjhavgbdjh" post.
I don't want to wander too far but a very related bronze badge could be:
Bronze: [bounty proof] Have a question remain unanswered after a bounty has expired.