There are many, but here are the ones I'm familiar with:

The Greenback party (1874-1889): They supported metal-backed currency due to concerns about inflation of paper money. It started on an agrarian platform and later morphed into the Populist party.

Socialist Labor Party (est. 1876): They supported worker's rights and unions. They essentially strive for a society without class disparity.

Know Nothing party (1845-1860): They basically wanted to eliminate "outside influences," which at that time referred mostly to immigrants (specifically Irish and German Catholics).

Readjuster Party (1877-1895): This party involved both Black and White Americans. They promoted a widespread public education system (for both White students and students of color). A lot of their platform had to due with the debt accrued by the south during the Civil War and "readjusting" the debt.

The Silver Party (1892-1911): Supported "bi-metalism" or silver standard/free coinage of silver. This overlaps with Bryan and his "Cross of Gold" speech. Independence Party (1905-1914): Formed by William Randolph Hearst! They argued for the Department of Labor and for a set work day.

Populist or "People's" Party (1891-1908): Farmers started the base of this movement. They believed that both the Rep and Dem parties were controlled by the banks and they wanted a third party to represent their interests. The Dem Party nominated William Jennings Bryan in 1896, in part, to represent populist ideals (needless to say he did not win).

The Bull Moose Party: This is cheating, because it's basically the Populist party reborn (1912-1916). Formed by Teddy Roosevelt, largely due to his increasing opposition to Taft.