"I was told at uni that sleep is cyclical and that as long as you wake up during the lighter part of the sleep cycle you will feel fresh and alert. Wake up during the heavy sleep part and you will be a like a bear with a sore head all day." -- John D, Glasgow, UK (from the comments of the article)

I have found this to be the case. If I wake up alert, I find it much easier to dive into a problem, which then keeps me awake.

I've noticed the same thing. I've been forced to wake up with an alarm clock at 6am for the past several years, but in the past (and I hope the future) I never used an alarm clock because it doesn't pay attention to my sleep cycle.

Okay..not quite all alarm clocks: http://www.axonlabs.com/products/smart.html

This was an accidental submission but it's a good read anyway. I know I rarely get eight hours; productivity ramps up at night for me.