Algebra and geometry, I feel, are still important today (see SAT). Greek and Latin are less important, although they are still in the background. The humanities have changed and we now learn about more modern authors / topics and the humanities classes in general have cooler names (i.e. Microcomputer Application in Kinesiology or Topics in African Society and Culture).
There's probably some bigger point I'm missing here like "those who don't learn from history are doomed to repeat it" or something similar.
Teaching kids about how to conjugate Latin verbs or some other rote activity always seemed pointless to me. Perhaps I'm preaching to the choir, but learning about entrepreneurship or practicing selling things would have been much more useful to me than many of the things I learned in high school or undergrad.