How Long???

The easy experimental answer to this question is 264 hours (about 11 days)^[1]^[3].

In 1965, Randy Gardner^[2], a 17-year-old high school student, set this apparent world-record for a science fair. Several other normal research subjects have remained awake for eight to 10 days in carefully monitored experiments. None of these individuals experienced serious medical, neurological, physiological or psychiatric problems.

On the other hand, all of them showed progressive and significant deficits in concentration, motivation, perception and other higher mental processes as the duration of sleep deprivation increased. Nevertheless, all experimental subjects recovered to relative normality within one or two nights of recovery sleep. Other anecdotal reports describe soldiers staying awake for four days in battle, or unmedicated patients with mania going without sleep for three to four days. (Read more of this article^[1] at Scientific American on-line).

The Australian National Sleep Research Project states the record for sleep deprivation is 18 days, 21 hours, 40 minutes^[2].

Sources

“How long can humans stay awake?” J. Christian Gillin, a professor of psychiatry at the University of California, San Diego, in Scientific American
Randy Gardner (record holder) Wikipedia
“Man Dies After Going 11 Days Without Sleep: What Are The Health Risks Of Sleep Deprivation?”, Huffington Post