How Significant Are Third Party Candidates in US Presidential Elections?

When the Republican Party's candidate, Abraham Lincoln, won the presidency in 1860, his was a minor party. Now, of course, it's one of our two main parties. But there are and have been many "third parties". Anti-Masons, Free-Soilers, Know-Nothings, Prohibitionists, Populists, Socialists, Communists, States' Righters and Libertarians-- they've all nominated candidates for president in the past.
America currently have five nationally organised third parties; Reform, Libertarian, Green, Constitution (formerly the US Taxpayers), and Natural Law. …