I am obliged to say math and science classes are important since I use those skills daily for my college education. Sometimes I do use the actual content I learned in high school (even imaginary numbers and what not), but I would say it's MEANT to make students feel comfortable with the subjects before they go to college and heavily build on those skills. I do admit that the content will not be very applicable in 99% (arbitrary number) of peoples' lives. But hey, these subjects do tend to exercise distinct skills, so maybe they can thought of like puzzles?
As for what's NOT important, it's hard for me to say. I did not try very hard in high school, but I regret it. I look back and think about how much I could have gotten out of it if I tried a bit harder.