The Star-Spangled Banner did not become the National Anthem until 1930. Until then there was considerable debate over what song should be the National Anthem. The most significant review of possibilities was performed by Oscar Sonneck, the Librarian of Congress, in 1908. He considered four songs:
At least three other songs could be added to the list since then. America the Beautiful was written in 1893, 15 years before Sonneck's work, but it was still not hallowed enough by tradition to be included. God Bless America and This Land Is Your Land were still in the future. Each of those songs would have advocates today.
This is by no means a definitive list and other people might include other songs. I left out Battle Hymn of the Republic and Dixie as from the Civil War period as too factional. But I think these are the core songs.