I have 13 answers on questions where the asker had said "this is what I'm looking for" yet they won't accept my answer using the check mark. What is a good way to ask them to accept without being rude about it?
Sometimes if it's a new user and they don't quite "get" the system yet, I leave a comment replying to their comment on my answer along the lines of:
@Whoever, I'm glad I could help! If this solved your problem, you can accept the answer by clicking on the gray checkmark under the answer's score. That way other people will know this worked for you.
However, there's really no way to compel anyone to accept your answer, and there are many questions that are going to forever be without an accepted answer for one reason or another. If you bug people too often, you're likely to come off as overly rep-focused, which is typically frowned on in the community. My advice would be to just learn to accept the lack of accept :)