"I teach them correct principles, and they govern themselves." - Joseph Smith, Jun
YES! YES! YES! In fact, if your child is over 8 and you're spending more than an hour or two a day actively working with them on "school" subjects, you're doing too much.
Kids inherently want to learn. You really can't keep them from learning. And they really like it when they *get* a new concept.
Math and history are the only "subjects" we spend a lot of "teaching" time on. Notice the quote marks....Math does tend to be learned in a vacuum, sort of separated from other subjects. History - well, it's a story. So for history I read them a story, and then encourage them to read other books from the library. Science? I cover it along with history and math, often with trip to the planetarium or the Bean Life History Museum at BYU, or one of the other wonderful museums in the area. Since I'm in Utah, I get the joy of having many resources available through the many universities.
The best way to teach at home, I think, is to teach them HOW TO LEARN. The most oft heard sentences at my house are the ones where I'm encouraging them to think instead of looking to me as the fount of all knowledge. Although I am brilliant (LOL!), I still want the kids to think for themselves. :)