I've never quite understood throw-away protest votes. The implication (in this case) seems to be that who ends up in the White House is irrelevant.
... or that it's less relevant than it is to send a message to the law-makers that one particular set of positions really matters to you.
For many people, I think the hope is that, for instance, the Democrats will look at the results and say "hey! Look at all those people voting for the Greens! If we strengthened our environmental position, we might be able to get them to vote for us!" ... and in the process, you might be able to influence governmental policy more than just voting for the Democrats in the first place.
Also, I think a fair number of people are thinking long-term, voting for a party that they know won't win
this election in the hope that their support will help the party build to that "critical mass" when other voters will see them as real contenders and vote for them instead of voting strategically.
Edit: also, I've been in the situation before where one candidate was a virtual lock and no other candidate had a realistic chance of winning. In these cases, voting for the second-place candidate wouldn't do anything to change the results, so I just vote for the party whose policies I most closely agree with.
Edit 2: another reason, though I'm not sure if this works with American rules: in some places, a party gets benefits based on how many votes they receive regardless of whether they win. Up here in Canada, I've known many people who have voted for fringe parties and candidates specifically to help them get to the threshold where they receive government funding.