Hello..............
Classical music is the basis for all music we here today. Take rock music for example: Your basic rock or pop song is composed of a verse, then refrain, verse, refrain, bridge/modulation, refrain. This is pure music theory. By studying the music theory behind this simple formula, you will understand why the chords work the way they work, why they sound the way they do, and where the music can lead you. You can also learn alternative progressions, rather than just the standard I-IV-V-I progression.
On top of this, by knowing music theory, you will be able to look at any piece of music and be able to analyze it. For example, you will be able to tell where the bridge is by a quick glance, what the song sounds like, and also be able to easily find mistakes.
All the good rock, alternative and other popular musicians have a good sense of classical music. I know of many who have, or currently study classical music, and classical voice training, including Mick Jagger, Steven Tyler, Cyndi Lauper, Christina Aguilera, and Billie Joe Armstrong (Lead for Green Day). They have spoken numerous times about the value of knowing about classical music and theory.