Third parties only hurt the party closest to them. They are a gift to their enemies. Ross Perot took enough votes away from George H.W. Bush for Bill Clinton to get elected. Ralph Nader took enough votes away from Al Gore for George W. Bush to get elected.
The third parties are drawn from the angry wings. Centrists tend not to go in for the kind of institution destroying that you would have to do to make a third party.
I see an asymmetry, though, between the two kinds of third parties. There are angry extremes on both ends of the political spectrum. Aside from tiny socialist sects, though, the left extremes hardly ever split from the Democratic Party to mount a third party challenge. The Nader campaign was unusual because he persisted in a vanity campaign into the general election, even when it was clearly hurting his own side. Contrary to the usual stereotype, it is Democrats who are more disciplined about working within the party. This is the advantage of a being a "big tent." On the right end of the spectrum, though, short-lived parties come and go all the time. Whether organized around a rich guy or grass-roots anger, libertarian and nativist "parties" keep splitting the right and undermining the Republican Party.
I believe there are more significant third parties on the right than the left because the right wing of American politics was born of the marriage of Protestant sectarianism and "you can't tell me what to do" individualism. Both sides of this family are good for creating motivating passion. But they are bad for sustaining political parties.