I know there's been pretty substantial discussion regarding Moderators being able to accept unaccepted answers, but the obvious issue with that is Moderator workload, purpose, and expertise. For an example just check out Moderators accepting answers on user's behalf after a certain time period
I'd propose that another direction be taken, after a period of say 6 months, the question is then opened up to users with a particular reputation level (you pick), and that after a certain number of these super-users vote to accept a particular answer, that the question be closed off as accepted.
This would address the workload issue by distributing it, it would address the expertise issue but requiring essentially peer review, and it would attack the growing problem of unanswered questions.
I believe an incentive could be awarded to those super-users for being part of an accepted answer to encourage the gradual cleanup of unanswered questions, maybe even a new badge of some sort.
EDIT: As I've mentioned in response to comments below, sometimes, the most upvoted answer isn't the best practice, as a user, I'd like to know what the pro's do more than what the masses do, and so in limiting this particular ability to those with higher rep would tend to lean in favour of a best-practice rather than popularity.
EDIT 2: I see that some have already decided that this is a duplicate simply because the question was asked, but my contention is that none of the others have proposed viable methods, I think this does, and it does it differently.
EDIT 3: The question of what if the OP still wants it open came up below, I would propose that the OP then have the ability to reverse the community selected answer, and lock it from further community closing's.
EDIT 4: Based on the discussion below, it's clear that this isn't just a repeat of past questions and that there are some good ideas here, I BEG those who marked this question as a duplicate to read on and reconsider so that we can continue to have a conversation on the merits, or at the very least point out why you don't believe it deserves to be heard out. I don't believe you gave it a fair shake.
Final Edit: Long live the popularity contest!