As chipmunk noted, a lot of this ground is covered by a recent poll. I find some relation to Maintaining one's focus as well since sometimes you can reach that proper state of mind from depriving oneself of sleep. Some of my best work was done during all nighters.

• How many hours of sleep do you get a night, and is it all at one time, or split into smaller chunks?

I've been out of work and started finding I sleep from 1 am to 9 am. Usually in one go unless one of the cats uses me as a trampoline.

• Do you have sleeping problems, and if so how do you cope with them?

I don't now.

• Do you feel that the studies on sleep are invalid and getting less sleep doesn't lead to illness and memory loss?

You can find studies showing lots of different conclusions. In the Oregonian recently they had a study that showed people functioned better if they got a short nap around 2-4pm. I don't remember if they tied in how much sleep these people were getting during the night.
One thing to note is that there are brainwashing and interogation methods using sleep deprivation.

• Can you be just as productive with little sleep?

No. For short periods of time it could work, but eventually I would crash.

• Are people adapting to busier lives by using something like caffeine and neglecting sleep?

People are trying. Caffeine is only going to keep you going for a bit. I've recently stopped drinking any caffeine for a diet I'm on, but I used to drink a lot. I do miss the aroma. Note: At "Job from Hell tm" my blood pressure was 150/110. Three weeks ago it was 120/80 and after stopping coffee intake it's now 102/64.

• Does a higher stress level affect your sleeping patterns?

When I was heavily stressed from one job, I found I had problems sleeping. My mind would be racing around trying to solve issues that I had no control over, etc... until I just dropped from exhaustion. The lack of sleep made me rather jumpy and irritable as well.

• At what point do we all become so infused with caffeine that our eyes will glow blue? :)

I once made coffee using Water Joe and Black Tiger beans. Black Tiger has 30% more caffeine than regular. Woke me up and I was fine until I had an Americano that afternoon. I was in a meeting trying to take notes, but my pencil kept shooting off the page. I did get a compliment about my eyes that day, hmmm.