Is it ok to accept your own answer on Skeptics.SE, and give it that green checkmark?
What does an accepted answer mean? Is there anything distinctly different between your own accepted answer, and accepting someone else's answer?
On one extreme, if your answer is unique, and it's a great answer (+100), then by all means do accept it.
On the other, if your own answer is a much poorer answer (-4) than someone else's (+13), then it accepting it in spite of the situation is abrasive to the community and you should clearly avoid such behaviour.
It only sends a "I am so biased that I only listen to myself" message to the community, so don't do that.
It's just common sense and respect for the community. Be a gentlemen, not a dick.
You can accept whatever answer you want, that decision is yours alone. Accepting an answer puts it at the top of the list regardless of its score, with the exception of self-accepted answers. Accepting an answer (that is not your own) also gives you +2 reputation, and the author of the accepted answer +15 reputation.
That said, accepting your own answers when there are good answers from other users present will be perceived rather negatively by many users. If you accept your own answer that is seen as inferior (as shown by a large difference in answer score), it will likely be perceived in a very negative way. If you think the community is wrong anyway, as they are obviously voting for the wrong answers, then why do you ask us in the first place? Such behaviour is disrepectful towards the community.
So you're certainly allowed to accept your own answers, but that doesn't mean it is a good idea to do that, especially if you accept an answer that is significantly downvoted.
Yes you can, the decision is yours alone. Who decides what the best accepted answer is? Jeff's blog says it best.
In case it isn’t clear, asking a question on Stack Overflow confers a few special privileges to you as the question owner:
(3). You can mark (or unmark) one of the answers as the accepted answer ...
That doesn't mean the community will agree with your choice. But as the question owner, it is your choice to make.
Or our own Fabian <> put it this way.
I dismissed the flag as I saw no reason to intervene. It is not our job to decide which answer is right or wrong. That is what voting is for. We only intervene in case of non-answers, which don't even try to answer the question.
The "accepted answer" feature was never intended to mark which answer is best or even if the answer is correct. It is, simply stated, the answer that the original author found most useful in solving their problem.
The people's-choice favorite answer is selected through the voting process. The "accepted answer" is all the original author. If you want to let the users also select the "accepted answer", the purpose of having a selected answer becomes redundant and useless. That decision has to come from the author, or you're just conflating the two features.
Voting already determines the communities "accepted answer." Accepting your own answer doesn't grant you reputation, or dock the answer below the question. If you are convinced that you know what is best for other people, step back and think why you feel so compelled that everyone agree with you. Why should it bother you that someone else accepts something that might be wrong ?