When I tell people that a major reason I vote for third party candidates is that I don't believe my vote really matters, they often respond with "Well, what if everybody felt that way." I don't know about "everybody," but I'm willing to wager that a significant number, perhaps even a majority, feel "that way." (And by the way, since we live in a "democracy," the majority is supposedly always right.)
Of course, what these people most likely mean is "what if everybody felt that way and acted on that feeling [presumably by not voting]." Although the rate of voter turnout is probably higher 'lo these past few years than, say, twenty years ago (I don't know, but that's my impression), something probably pretty close to a majority of people eligible to vote do not vote, so I'm not sure that a lot of people don't act on that feeling.
Still, the point is not that there are not a lot of apathetic, disaffected people out there--I think they'd be willing to concede that--but that voting matters and we must make our voices "heard." Okay, so, in a large contest (say, a presidential election, any statewide election, or city-wide election in a large or even medium-sized city), my one vote, out of several thousands cast, is going to make my voice heard.
So, to take a made up number, let's say that I vote for Mr. Obama, and he wins over Mr. McCain in Illinois this November, and the final tally is 371,852 to 302,501. (Let's also assume that every vote cast is counted, something highly unlikely, even if it weren't for Illinois's rampant corruption, because there are bound to be anomalies in the vote count.) My "voice" is heard loud and clear. Mr. Obama, instead of winning by a vote of 371,851, will have won by a vote of 371,852.
Now, there is the highly improbable, but still possible, situation wherein a candidate wins by one vote. In that case (again, assuming all votes are counted as cast), then yes, my vote would have an effect on the outcome. So, back to the Illinois example, let's say the vote turns out to be 371,857 (Obama) to 371,856 (McCain) , and that I vote for Mr. Obama. (Let's also assume that the automatic recount is done and the exact same result carries over.) On the surface, it appears that my vote matters. Yes, Virginia, I guess it does. Still, it only matters because 371,856 other people voted as I did. In order for my vote to matter, hundreds of thousands of people have to agree with me. I need to be on the side of the pro-Obama cheerleaders in order for my voice to be heard.