This topic has come up occasionally in other posts, but I found no question on the site asking about this specifically.

In 1834, ED Howe published Mormonism Unvailed [sic], claiming based upon the work of Philastus Hurlbut that the Book of Mormon, published in 1830, plagiarized an earlier work of Solomon Spaulding entitled Manuscript Found.

Most proponents of this theory suggest that Sidney Rigdon served as the connection between Solomon Spaulding and Joseph Smith, who Latter-day Saints believe translated the Book of Mormon from an ancient record by the gift and power of God (source)

Spaulding died in 1816 without having completed or published Manuscript Found; from his own correspondence we know he was working on the manuscript in 1812. The manuscript remained in the possession of his family until the 1830s. The manuscript was lost for several decades and was rediscovered in 1884; the popularity of the theory declined after this time.

How do Latter-day Saints respond to the Spaulding theory?

Background on Solomon Spaulding's manuscript and the theories associated with it can be found here.