There are several layers to this problem, and it is an important problem because understanding is the first step towards making rational decisions.
Rounding up, Obama got 66 million votes and Romney got 61 million. Your one individual, insignificant vote is like one individual molecule of the drop in the bucket. It simply won't change anything one way or the other.
"But if no one votes, then the terrorists win." I understand that people need to vote in order for there to be an election, I'm just giving you the reality of the situation.
Now, obviously something does matter, because elections are successfully held and candidates win or lose for some reason or another, it's just not because of your vote. When the American people (or any people) vote in legitimate elections, the votes individually do not count but they create a milieu, so to speak. A milieu which can be exploited.
So if individual votes don't matter, then what does matter?
Well, for some background let's hop into the Wayback Machine and travel all the way back to the mid 2000s when a little group called Citizen Change was trying to get young people to vote with the slogan "Vote or Die". Now, on the surface this almost seemed to be a non-partisan drive to increase voter participation, but was it? No, because the reason this group was trying to drive young people to vote is because they expected young people, freshly indoctrinated by public education, to vote for Democrats.
Do you really think anyone cares when young, uneducated know-it-alls vote? No, unless they know those young folks are going to vote the way they want them to. That's what they care about.
And that matters. If you can mobilize a demographic of people to all vote for the same person, then those otherwise insignificant individual votes become very important by sheer volume. One vote doesn't matter, but 200,000 votes matter, and 1,000,000 votes certainly matter.
This is why movements like the Tea Party and so on have become such a big deal: individual votes do not matter, but collective votes (movements) do.
"So my vote does matter, as long as I'm convinced to vote as part of a collective?" No, even if you are a Teabagger, and you were convinced to vote for a Republican by the movement, whether or not you as an individual vote still doesn't matter. Nothing will change this fact, ever.
In fact, the person or group who organizes these movements now wields a large number of votes via the collective, and so they effectively get to have the combined voting power of everyone they convince to vote in line with their agenda.
The movements matter, and have a real effect on election outcomes. But of course, something matters even more than any individual movement: The status quo. For instance, in America we are (almost) all Statists. We all want to wield The State as a tool to achieve our political and social ends, and every election revolves around Statism.
This status quo of Statism has an even bigger effect than possibly all movements combined, and in fact all movements are typically created to achieve the ends of the status quo. But how do we know this status quo is so powerful? Because both of the two main parties are nearly indistinguishably Statist; there is no variety, and they must both work to further the Statist agenda. That status quo controls the candidates who run, because any candidate must fall in line with the status quo in order to have any hope of winning. Lately the Republicans haven't been the right kind of Statist, and so they have almost no hope of winning the Presidency in the short term unless something changes.
Yes, Democrats might be Statists about unique issues like women's rights, or welfare, or homosexual rights, but Republicans are Statists when it comes to crime, and so forth. They mostly differ in their philosophy of how the State should control people's lives, that's all. But since we tend to switch up who we vote for, in the end both agendas get a say and, ironically, the Statist status quo is advanced even quicker by the variety.
Whenever I hear a Republican talk about "smaller government", all I really hear is, "We need a leaner, more efficient and cost-saving way to control people's lives." That's all. The real size of The State, measured by its influence, will never be reduced by Republicans even if they somehow, miracle of miracles, manage to reduce spending and bureaucracy.
There are exceptions here or there, but in general this rule holds.
This is why your vote does not matter, you're simply dwarfed by people with the power to start political movements, and the popular consensus of Statism. You cannot compete with that or change anything with your single individual vote.
If you want to really change things, then you need to either convince someone in power to push an anti-Statist agenda, or you need to become powerful yourself and start a movement that challenges the status quo. But please, stop posturing and pretending like you're an amazing person for voting and shaming other people for refraining from voting. No individual vote will ever, ever matter.
And now you know about the dark side of democracy. But effective change can be made, it's just going to be more difficult than putting an "X" inside of a box.