Sometimes a well-posed question appears and makes one really think. And while the original intention of bounties was encouraging others to post an answer that may require above average effort, the option "reward an existing answer" made me think - formulating the question itself may sometimes deserve a reward as well, and not just the "oh yeah, nice question"-upvote - in fact. And while an added bounty may yield additional upvotes by others, I'd still like to propose the implementation of one of the following:
a) The option to award a bounty to the question in addition to answers
b) Part of a bounty awarded to an answer is (optionally) awarded to the question as well
I think option a) is straightforward, although in that case an additional option "reward the question" that is either assigned immediately (so the question doesn't show up in the featured list) or automatically after its expiration (so the question is additionally rewarded by being featured) may be useful. But it should also be possible to award a usual bounty to the question in case no helpful answers appeared.
Option b) could be implement in various ways. One possibility could be that a non-OP bounty causes the question to automatically obtain part of the bounty, say 10%, additionally to the actual bounty, which is not deduced from the bountyee. But it would be better to set this percentage manually, since sometimes one wants to reward an clever answer to a question that doesn't really deserve a bounty as well.