US political history is dominated by two parties and our first-past-the-post system essentially guarantees that won't change. However, at times when we've experienced major party transitioning like the split of the Democratic-Republican Party and the collapse of the Federalist Party, were there meaningful periods when three major parties existed?
2nd Edit: Yes, here are three parties that existed that were popular.
The Bull Moose Party: (1912 - 1916, think Teddy Roosevelt)
The Whig Party: (1833 - 1860, think Henry Clay and William Henry Harrison)
The Know Nothings: (1845 but not fully through 1860, think Millard Fillmore)