If you basically like your country's political system as it is, then voting helps keep it that way. Having large numbers of people at polling places at election time is a show of trust and civic participation. It means that we're still invested in our institutions and political traditions. Even if your vote doesn't count much to sway outcomes, your presence at your neighborhood polling place is visible to your neighbors and does increase the sense of community participation.
Of course there are compelling arguments that "civic religion" is a bad thing, but if you think it's a good thing, then showing up to vote does help.
Having large numbers of people at polling places at election time is a show of trust and civic participation.
I suspect that the opposite is true. It seems to me that people would be less likely to vote if they trust their fellow citizens to make the right choice and believe that the political system is fine. Turnout was at its highest in 40 years in 2008, in spite of the fact that most people agree there was a profound amount of political distrust and acrimony in that election.
For many years I've been interested in the "paradox" that your vote tends to never alter the outcome of an election, yet the outcome is in fact determined by the votes. I wrote a blog post about this and tried to explain it in terms of emergence, we as voters are just feeling what it's like to be just a tiny part of a much bigger system.
Then I tried to explain that "voter turnout" is in fact one of the most important metrics for an election, it determines the legitimacy and stability of the process. So therefore even though your vote won't determine the winner, it will contribute to voter turnout and thus is productive and useful.
http://www.kmeme.com/2010/10/why-you-should-vote.html
However I don't find my argument all that compelling, because even voter turnout is going to be approximately the same whether you vote or not.
In the post I bring up littering as something else where your tiny contribution adds up to be bigger result. I personally would never litter on purpose, yet I often skip voting because it seems like it doesn't make a difference. Is voting rational? How do you justify voting or not voting? My post was non-partisan so I'm soliciting non-partisan comments, trying to focus on the theory behind voting in general.