In addition to Dvorák and his comrades (see Bohemian composers), the following are worthy of note:
George Chadwick (1854-1931): the best of the American composers' circle, who lived in Boston around the turn of the century. I recommend his chamber works.
Samuel Coleridge-Taylor (1875-1912): son of a physician from Sierra Leone who married an Englishwoman, Coleridge-Taylor considered himself a follower of Dvorák, although his oratorio, Hiawatha, sounds rather like Mendelssohn. He also wrote an excellent Clarinet Quintet. In Washington, D.C., a 200-voice African-American choir was formed, and named in his honor, to perform his works.
Ernö Dohnányi (1877-1960): an Hungarian protegé of Brahms. His son, incidentally, was a resistance fighter against the Nazi regime in Germany.
Hall Johnson (1887-1970) and Harry Burleigh (1866-1949): these two composers/arrangers elevated the American "Negro Spiritual" to an art form, on the level of the German Lied. Look for recordings by Marian Anderson.