The first was formed by Theodore Roosevelt in 1912. Roosevelt ran against President Taft in the Republican primary, spurred by bitter resentment of the policies of Taft, who had been Roosevelt's hand-picked successor. After Roosevelt was defeated in the primary, reporters suggested that he was no longer fit for the office. Retorting that he was "fit as a bull moose" (giving the party a nickname), Roosevelt ran on the Progressive Party ticket in the 1912 Presidential election. Roosevelt had the satisfaction of defeating Taft in the popular vote, and by a large margin of 88-8 in the electoral vote, but the split engendered in the Republican vote allowed Woodrow Wilson to win the presidency.
The second was formed under the leadership of Robert M. La Follette, Sr of Wisconsin, another erstwhile Republican, in 1924. La Follette's politics ran toward the socialist end of the spectrum; he favored public ownership of railroads, etc. His run for the presidency under this ticket garnered 17% of the popular vote, but carried only one state (Wisconsin).
In 1948, another Progressive Party was formed toward the end of electing Henry A. Wallace president. Wallace was yet another former Republican, who had nevertheless supported Alfred E. Smith in 1928 and Franklin Delano Roosevelt in 1932. The party adopted a pro-Communist viewpoint. Wallace's campaign garnered no electoral votes and less than 3% of the popular vote. Wallace later renounced his pro-Communist stance.