I put the classics into the rotation, but they are by no means my focus educationally. I think they should be read because there is quite a bit of cultural literacy surrounding them. However, I am frankly somewhat horrified by the lessons taught by many of them.
For instance, I read my dd Jack and the Beanstalk the other day (it was part of her Moving Beyond the Page curriculum). For those of you who haven't read the full original version recently, Jack (somewhat foolishly) trades his family's only hope at sustinence for some beans, then climbs the beanstalk grown from them and repeatedly steals from the ogre (who isn't nice or anything, but the wife is, and besides the ogre never did anything bad to Jack directly) until he has stolen enough to become rich and then he marries a princess.
When I finished reading it, my dd said, "That is the worst story I have ever heard!" LOL, out of the mouths of babes...not the kind of morals/ethics I'm trying to instill in my kids, needless to say!
I completely agree that kids should be familiar with the classics, but they are more of a "side show" in the literature realm for me, I tend to choose what I would consider higher-quality literature as my main focus.