A large proportion of discussions relate to problem solving. And a huge benefit of having a forum is the archive of discussions which act as a useful resource for people.
When people come to forums, we encourage them not to post the same old questions again and again, but rather use the search facility to find existing threads. The reader will then be focussing on finding the best answer to that question.
With these facts in mind, having a thread where the best answer is easily accessible is a very useful feature. The first post has the question. The reply voted the best answer is then displayed immediately beneath (perhaps expanded via a nice ajax widget). It saves an enormous amount of time for people wanting to find the solution to their problem. Your forum immediately becomes a much more accessible resource.
The problem is identifying the threads which actually have a question and which are appropriate to display the best answer. There are many examples of threads where it is not appropriate. How do we decide? Do we have it as an option for the thread owner?
Also how do you calculate the best answer? Maybe someone replies with one answer which gets 20 'likes' and then someone replies with a better answer which has only 10 because it has had few views being newer. So maybe a more intelligent algorithm is needed which takes into account the proportion of likes to views?
Should we even use the 'like' system? We could 'like' a reply for many reasons, not necessarily because we think it's the best answer. Maybe it's particularly witty.
Lots of questions making a good 'best answer' system potentially quite complex.
However, this is functionality which I have been considering for AVForums for some time as it is clearly extremely beneficial.