In nearly every election of a state official, even those in which only a few hundred voters participate, the margin of victory is more than one vote. What that means is that, if any one voter had refrained from voting, or if any one abstaining voter had not abstained, the candidate who won would still have won. Some people — even some very intelligent people — conclude that the vote of an individual has no efficacy beyond that of other acts of expression. Those people are missing something.
Indeed, one's vote or refusal to vote has absolutely no effect on the election at hand. There are various things that one can do prior to the election which may help one candidate to achieve a margin of victory, or prevent another from achieving such a margin. But one's own vote isn't going to make any difference in that election.
However, as potential candidates and parties decide what to do with future elections in mind, they look at margins of victory in past elections. Potential candidates decide whether to run and, if they choose to run, how to position themselves, informed by those margins. Parties decide their platforms and whom to nominate, informed by those margins. With large margins in their favor, they feel free to alienate a greater number of potential voters; with small margins or losing margins, they consider what to do differently in order to pull voters who previously voted for another, or who didn't vote at all.
Thus, an individual vote or the decision not to vote has a small effect — but its only effect — on later elections and on behavior of those who are acting with concern for later election.
The least effective thing that a potential voter can do is to vote for a candidate whom he or she dislikes. People in America who have held their noses to vote for the Democratic or Republican nominee in order to stop the nominee of the other party did worse than to throw-away their votes; they have helped to ensure that the next pair of choices would likewise be disagreeable, and that the behavior of officials in the mean time would likewise be disagreeable. It is only if one genuinely thought that one of these candidates were worthwhile that one should have voted for him or for her, and then still only to affect the next election and interim behavior of officials.
The most effective thing that a potential voter as such can do is to vote for a candidate of whom that voter approves, even if that candidate has no chance of winning, or to submit a ballot from which no candidate receives a vote. An increasing number of people are doing the latter, either in expression that no candidate is worthy, or to challenge the legitimacy of the process in a way that makes it difficult for these people to be dismissed as apathetic by apologists for the process.