Basically, I want to know if it would be humanely possible to sleep one day, skip the next, sleep, skip, sleep, skip, etc, with a 8 hour sleep time.
If you need any extra information, let me know.
I'm not aware of any study testing this hypothesis. I would surmise that adverse health effects are likely because the circadian clock operates on a 24-hour time frame, and because lack of sleep for ~40 hours every second day will alter hormone, cytokine and other measures to levels not normally seen in 8-hour sleep/16-hour wake cycle.
(too long to be a comment)
You may be interested in http://en.wikipedia.org/wiki/Phase_response_curve.
This graph shows how the body's circadian rhythm normally works: http://en.wikipedia.org/wiki/File:Body_Temp_Variation.png. Body temperature decreases during the night (apparently due to more melatonin production.
I conjecture that the proposed schedule would interfere with the Circadian rhythm. Melatonin is the hormone that regulates sleep--it causes drowsiness. It is suppressed by blue light (because we get exposed to blue light in the daytime).
Aside from this, I am also very interested in the effects because I have personally wondered about the same question. The thing I am worried about is significant immunosuppression.
A larger question might be--"Why is sleep necessary?" Does it serve only to conserve food (which is very useful if you are living on subsistence) or does it serve a greater purpose? (whenever I have asked anyone about it, they always cite "regeneration" and some have cited the recycling of neurotransmitters. Personally, I'm a little skeptical.)
One final study: there was a study by Dement on the effect of dream deprivation: he took several people and woke them up whenever they went into REM sleep. Then, there was a period when the patients were not woken up. He found that there was a "REM rebound"--that they would go into more REM sleep after they had been deprived of it. This seems to indicate that dreaming, specifically, may serve a significant purpose.