I suggest that we award bronze, silver and gold badges to users whose answers have been accepted x,y,z number of times. Self-accepted answers don't count.
This would encourage everyone to put more thoughts into their answers, and improve the quality of the answers as a whole
I'd like to provide a different rationale for supporting this badge (and I'll let the auto-bounty awarding mechanism thing decide).
A set of badges for X, Y and Z accepts would make for a fun goal users can work toward; I would put it more in the same league as Epic and Legendary. The existing accept-based badges, as @Koper noted in a comment, are more luck than anything else: you basically catch a popular question, and come in early with a solid answer.
Badges for number of accepts would reward a user's quality activity over a longer period of time.
Acceptance already comes with a 15 point reward and is part of the qualifications for Enlightened and Guru, so it is not like there is no incentive at this point.
I'm not strongly against the idea, but it does not seem important to me.
I think this is a good idea. As a relatively new SE acolyte it seems odd to me that there is no badge directly tied to the amount of accepted answers. It seems logical that the goal of answering a question should be to provide one that the asker finds satisfactory. SE seems to already support that ideology by awarding more reputation for an accepted answer than a upvote, so I'm surprised that there are basically no badges directly tied to this.
It seems strange to me that a user could potentially piggy back on high volume questions providing supplementary answers and get a lot of votes but not contribute to satisfying the site's question base (not to say that supplementary questions are bad). I'm just saying that I think it makes sense to provide incentive to not only display knowledge and popular opinion but also to reward good listeners and problem solvers that are aiding in the site's overall purpose.
