Here's how answers to a question on Stack Overflow appear to the questioner:

When the questioner clicks on one of those checkmarks, it marks the answer as the accepted answer to that question, and changes the checkmark from a gray stroke to a green fill.
Everybody else reading the question will see, below the questioner's name, an indication of how many of their questions have accepted answers. Today, for example, my questions have:
Peter Hosey
23.1k •2 •14 •28
67% accept rate
This indicates that I have accepted answers on four-sixths of my questions.
Sometimes, I see a comment like this semi-fictional example (written by me, based on several real examples I've seen) on a question whose author has a low or zero acceptance rate:
0% accept rate? You really should accept answers on your questions, or people may not answer any further questions from you.
This is a bad reason to accept answers.
The real reason to accept an answer is that you believe it's the correct answer.
Sometimes questioners choose bad answers (deprecated APIs, hacky solution, etc.). When that happens, it's a problem because it may lead future readers astray—they may think that this is the correct answer (because the questioner said so), without reading the other answers or the comments and finding out that this way sucks and/or there is a better one.
The same problem happens when a questioner accepts an answer because they think they have to, out of some sort of social obligation, rather than because they truly believe it is the correct answer. They may not have the correct answer yet, or there may not be a correct answer yet, but they feel like they have to accept something, so they accept the best answer they have, however good or bad it is, solely to raise that all-important number.
That sucks.
Questioners: About a day after asking a question, you should return to it, read all the answers, try them in descending order by votes, and accept the one that works and is the least hacky, for the benefit of other people who have the same question you asked. Take comments into account—something may not look hacky, but a comment may point out the hackiness.
And if there is no good answer, you don't need to accept anything. For the same reason (the benefit of future readers), you should leave the question open.
It's OK to have an acceptance rate that is below 100% or even low, as long as you are accepting answers that you find work and are non-hacky, on as many of your questions as you can. As long as you're making that effort, you're doing it right.
People who post comments like the one above: Why are you so desperate for karma? It's not like it's scarce or valuable. Net scores on answers are meaningful (usually), but your personal total, like mine, is next to meaningless. It's a reward, yes, but an empty one, so I don't see why you get all hurt when you perceive a risk that someone may not give it to you.
In summary: Don't worry about it. Accept correct answers, write correct answers, and don't worry about your acceptance rate or anyone else's.