From the time they were toddlers, I've involved my kids in the best, most challenging, mind-expanding extracurricular activity around (and it's free!): boredom. Our family needs a lot of unplanned, unscheduled time to maintain our balance, so at the moment there are no sports, no music or language classes, and only the occasional playdate. Instead: lots of time outside climbing the tree or playing "hot lava monster" with the neighborhood kids (now that it's finally sunny) or inside drawing, playing board games, reading, and an hour of Gameboy or TV.
As much as I know our family needs a slack schedule, my kids don't always appreciate it. There's a fair amount of whining, "What can I do now?" If I can restrain my impulse to get irritated, I remember that's the signal their imaginations are about to kick in.
Over at Parentingideas.org, Crissy sent in a bunch of articles on the value of downtime. I enjoyed the Family Circle article — well-written and reasonable. Another one of the articles had a great retort for "I'm bored!" (unspoken rest of sentence: "and I want you to fix it!"): "Congratulations! Now you have some time to find out what a special person you are."
In January I wrote about Blessing of a Skinned Knee: a kind, wise book that extolls the virtues of boredom and other discomforts.