On Stack Overflow, accepting an answer provides valuable feedback that a question has been answered. It completes the loop helping us distinguish a satisfied customer from someone who didn't get the information they were looking for. As Jeff says:
The question owner is not required to accept an answer to their question. We view accepting an answer as a simple social convention, a little informal "thank you" between the asker and answerer, a virtual tip o' the hat to that person whose response, as the question owner, you personally found the most helpful.
That doesn't mean the community will agree with your choice. But as the question owner, it is your choice to make.
We've gone over a year with this system and it hasn't really caused any major problems as far as I've seen. People generally get that the "accepted" answer isn't always the best answer. We've also done more to focus the site less on "truth" and more on facts, which make divergent, but correct-in-their-own-paradigm, answers less common.
However, we still have a system that looks odd to a new user. I've heard anecdotal evidence that new users are confused by the current system. We are not a church, but at first glance the presence of "Accepted" answers that get a little tick of approval could make it seem like we are or have aspirations to become one. Nevermind that answers are sometimes accepted in the face of community opposition; we are used to Christian sites trying to assert Truth. It gives the impression that we are less pluralistic in culture than we really are.
I have no idea if the Stack Exchange network development team will be interested in changing the system to support this site. There's a strong argument to be made to leave well enough alone. Please vote this question up if you feel there's a problem with Accepted answers on our site and vote it down if you think everything is working out fine. Also, please provide any suggestions that might require developer support in the form of an answer.