Kids that are overly tired have difficulty remembering what they learned. They are more inattentive in class and can be more impulsive (sound like a frequently used diagnosis to anyone?). Furthermore, kids who lose sleep don't have the time needed to process what they've learned during the night making the information harder to retrieve or risk not having it "stored" in their brain at all.
So where does this leave us as over-scheduled families? Have a sleep routine and stick to it. Try to be as consistent as possible with younger children. Engage in a conversation with your teen to negotiate appropriate bedtimes that can be agreed upon. There's a way too much going on in their brains during sleep to risk cutting this time short.
The studies I mentioned in this article were published in Po Bronson and Ashley Merryman's excellent book Nurture Shock which I highly recommend picking up. Now turn off your computer and get some sleep!