I've noticed that there are quite a few users with very low or no acceptance rates on the questions they have asked, and most of the questions have good answers. It seems that this is counterproductive to the purpose of the site if good questions have good answers and they don't get accepted. Is there some type of accountability to prevent users from leeching off the site and never accepting good answers, even if they have been asked about the non-acceptance? What's an appropriate way to approach the issue? I've looked but haven't found a suitable answer to this in the FAQ or in the Great Outdoors meta.
Unfortunately, no. There is nothing to force users to accept answers, just the 2 rep they receive to gently encourage them. This issue comes up fairly often on the main network meta site, meta.stackexchange.com, and the community team's response is always similar: "there's nothing we can or should do to force people to vote or accept answers."
Remember, whether your answer is accepted or not, you get +10 rep for every upvote, so you're still better off answering questions than not. The rep for an accepted answer is little more than icing on the cake.
Perhaps it's just me, but I never actually got the great outcry that people always seem to make about users not accepting questions. Yes, it can be mildly annoying, especially if a question has in fact been answered fully - but more often than not, the best answer will be bumped up to the top anyway via votes, so will get seen by the majority of people who visit that question.
I'm not sure many people will write a question and its answers off because there's no accepted answer. If anything it can often go the other way - I've seen people accept any old answer, bumping that to the top, whereas in fact the best answer is the one with more votes that sits below the accepted one!