American music has been affected by African American music to such a degree that it would be hard to think of what American music would be like without this influence. Most forms of American music today come directly out of African American musical forms and even those that do not have been heavily influenced by those forms.
Two of the main musical genres today are rock and hip-hop. Both of these come directly from African American styles of music. Rock has been around longer and has evolved away from its roots to some extent, but it had its origins in the "race music" of the 1950s. Hip-hop is much more recent and comes directly from African American styles of music of the late '70s and early '80s.
A third major genre is country music. This does not come directly from African American music. However, this music originated in the South where it was impacted heavily by African American music. In addition, the banjo, a quintessentially country instrument, was created by slaves in the Old South.
In these ways, essentially all American music has been influenced by African American music.