The Science of Sleep

http://www.supermemo.com/articles/sleep.htm#Free%20running%20sleep
http://www.supermemo.com/articles/polyphasic.htm
http://harvardmagazine.com/2005/07/deep-into-sleep.html

Wow, 'sleep', actually 'sleeping properly', is incredibly important for the general well-being (social, professional/academic, health) of a person.

The advice from the above articles is - if you can, sleep when you feel sleepy and sleep until you wake up naturally. Alarm clocks are not good for our health.

From the above articles, I learnt that we have a 'body clock' and it may or may not operate on 24 hr schedule. Sometimes it might be 25 or 23 etc. This will result in a person not being able to sleep/wake up at the same time every day.

So, are we doomed if our body clock is 'off' ? Answer is No. It can be adjusted.
From The Complete Guide to Natural Sleep:

If you usually have trouble getting to sleep, take an early-morning-walk in sunlight, or if you live in a sunless climate, expose yourself, particularly your eyes, to strong-artificial-light. Light-in-the-morning, tells the pineal gland to emit melatonin early-in-the-evening, so that you feel sleepy when you go to bed. Melatonin is the sleep/wake hormone.

Conversely, if you are going to sleep much too early, try the technique of delaying your internal biological clock by standing or walking in sunlight or strong artificial light in the later afternoon or early evening.

And if root causes are stress, non-stop mind-chatter etc - solutions suggested include:
- writing down problems and solutions on a paper just before sleeping (Abraham Lincoln's strategy)
- a couple of drops of Bach Flower White Chestnut

Edit - Article on finding solutions during sleep - http://www.miamiherald.com/news/politics/AP/story/1088029.html