The greatest triumph of the two political parties in this country is that people really believe that if they don't stamp R or D on their ballot they are throwing their vote away. That no matter how bad one of the candidates is, if he's a little better than the the other candidate, the one who can't win at any cost. The ruling parties have convinced American voters that it's a binary decision.
That frankly, is a load of crap.
The two major parties spend a lot of time pandering to enough different people to ensure enough votes to win. They don't necessarily look out for people's interests, but they make a lot of speeches suggesting (or outright saying) they will. Then they get into office and vote the party line, occasionally listening instead to a wealthy donor or lobbyist. The two parties spend most of their time talking on topics where they differ and spend most of their time voting exactly the same. Yet, the American public is convinced only a candidate from one of the ruling parties can win, and that voting for anyone else is like voting for no one at all, or worse yet, supporting "the other guy".
Choosing the lessor of two evils is still choosing evil. To me, that's wasting my vote. I'm going to offer a very good reason to vote for a third party candidate, even if that candidate has no chance of winning.
It's the only way your voice will be heard in the election.
If you aren't a millionaire donor, a lobbyist or part of the political machine, there is little you can do to influence politicians. I've been known to write letters to my representatives and frequently only get form letters back. Some aid scanned my letter to look for key words, then picked the appropriate form letter to send back. So how can I influence them? Giving to political groups is one way, groups that collect the money from thousands or millions of members and use that to lobby. But there is a cheaper way.
Vote for somebody else.
How does that work? Well, look at history. Every time a minor political party starts to gain some traction, one (or sometimes both) ruling parties take enough of their ideas to win back the voters they lost. This is how the environmental movement gained ground so quickly. They felt strongly enough about issues they broke from one of the two major parties and started supporting other candidates. This cost some people elections, not to the 3rd party most of the time, but to the other major party. This gets the attention of party leaders. Democrats lost enough votes to the Green party, they had to embrace some Green party ideals to get those people back. Do you wonder why there isn't a larger Socialist party in this country? Again, the Dems adopted enough of their ideas to keep voters in their camp. You see it the Republicans as well, any district where the US Constitution party or US Taxpayer party would start to gain traction, the Republican candidates would start pandering to the people who support those parties.
That's how we can effect the major party platforms, by voting for someone else. If you are tired of war, vote for an anti-war candidate, there are several running. If you are tired of government bailouts, vote for a candidate that stands against that. (I know of at least one candidate that doesn't support those) If you are for more redistribution vote for a Communist candidate. If you are for legalization of pot, vote for a candidate who supports that, like a Libertarian candidate. If you want the government to get more involved in environmental causes vote for a Green party candidate. It's the best way you can affect the platforms of the two parties in charge. If enough people stray, they'll need to change to get them back.
This holds especially true in elections where one side is highly favored. If you support Obama or Romney, but live in a state that's locked up one way or the other (which more than half the states are) cast a vote in support of ideals that really matter to you. If live in New York and you support Obama who has New York won easy, but want an end to the war in the middle east and the war on drugs, a vote for Gary Johnson makes a lot of sense. If you live in Wyoming and support Romney but think the US needs more consideration to environmental issues or animal rights issues, vote Green party. If Johnson or another 3rd party candidate pulls in a fair percentage of the popular vote then the ruling parties are going to have to at least consider including parts of their platform to get those voters in the next election. Otherwise they know that a 3rd party left to grow has the danger of upsetting future elections for R's and D's. They don't want that. They do need your vote.
Also, it's a great way to feel good about yourself when you leave the polls. Why vote for a scumbag just because they are a bit less scumbaggy than somebody else when you can vote for someone you believe in? Especially if you are in an area that leans heavily to one side or the other, casting a vote for a candidate that's going to win by 30 points in your district is wasting your vote. Voting your conscience isn't.