Boredom comes in two forms (that I know of):
1) Good boredom, the kind that consists of uneasy restlessness as one searches for what to do next?
2) Bad boredom, the kind that occurs when you're trapped in a deadly meeting or class and have to pay at least superficial attention, so your brain can't veer off on a productive tangent. This can make you crazy.
Both Andrew and I experienced a lot of bad boredom in our elementary school days, and both of us put our unchallenged minds to use by being difficult in middle school. (Yes, I filched a package of to-be-dissected worms and artfully arranged them on the English teacher's plate of spaghetti!) Good boredom, the kind that comes from unstructured time, kept me sane.
Kids come in many flavors, from the self-entertaining to the always-need-to-be-engaged. Based on my sample of n=5, I'd guess that the spectrum correlates roughly to the degree of introversion in the child. Then again, since I don't want a career in the entertainment industry, I tend to be very consistent about replying to any moan of "What can I dooooo?" with a cheerful, "You can clean the bathroom..."
Still, there are times when a child isn't able to use boredom well. We had an incident yesterday where one of my kids could only think of two things to do, neither of which was possible at the time. After a while this child came up with an alternate activity: tormenting siblings. That produced a rapid-fire series of entertaining responses, both from the siblings and from Mom.
Today Mom will expend some energy finding better forms of excitement.