I believe in boredom. I like entertainment occasionally, too, but I tend to think that part of the reason America has lost its creative edge is because we've overdone it on the entertainment front. We've stopped allowing ourselves to writhe through that uncomfortable, foggy, what-can-I-do period, so we never come out on the other side of it with fresh ideas.
There's bad boredom, of course. That happens when you're trapped in a situation and can't escape and have limited ability to use the time creatively, like in dull lectures or endless meetings. But the boredom of free time in which you've exhausted all the usual things to do and mope around and pick up things and put them down and whine to your mom (who only suggests cleaning the bathroom)... that's the boredom that finally results in innovation.
I recently heard someone who's on the advisory board for the Cogito website speak. He said that as they were developing the web site, the first thing the board of scientists and inventors and entrepreneurs were asked to do was make a list of what elements (books, coursework, experiences, etc) were essential for creative thinking. Every person in the room listed the same thing as #1: free time. Time to think, time to play with ideas, time to explore. This makes total sense to me.
Not all kids are good at being bored. Extroverts tend to do their best thinking while with other people; some kids need lots of structure; other kids simply flounder when left to themselves. But I think we do a disservice to our kids when we don't allow enough unstructured time for them to find their own way through boredom. If entertainment is the main solution we offer, we aren't teaching the next generation the skills they'll need to solve other kinds of problems.