What happens if you answered your own question and no one else did? You can't 'accept' your own answer, can you?
Possible yes, weird usually, rarely it is the best.
But, sometimes one has a question that one spends time answering (before getting to ELU), but then you realize that the Q/A might be helpful to others. Also, sometimes the answers create a number of partial answers and it is nice to have a single unifying answer which often the questioner is the best one to make.
That said, for the most part it looks weird.
And you don't get the 15 pts (otherwise you could create questions all day and accept them yourself and increase rep arbitrarily). You get rep for -others- voting on your answer but just not the acceptance points.
Yes, you can accept your own answer.