Which music genres were influenced by classical music?

Everything! The same theoretical elements of western music are used for all sorts of music: Jazz, Pop, Latin, Gospel, Musical Theater, etc. When we think of classical music, we usually tend to only think of Bach or Mozart, but these composers actually influenced the theroetical understanding of how music functions and how we as listeners interpret the music. Just think, without Bach there wouldn't be a Beyonce, or a Kesha, or whomever.