A good book to read about this is Sleep Thieves by Stanley Coren. He tells a few stories of people who tried to sustain wakefulness.
One famous case is the disc jockey Peter Tripp who in 1959 stayed up for more than eight days as a promotional stunt. After a few days, he began to hallucinate, seeing kittens, mice, and cobwebs. He also became paranoid, insisting that an electrician had dropped a hot electrode into his shoe.
In 1964 high school student Randy Gardner (17) attempted to break the Guinness Book of World Records for the longest time awake -- 260 hours. And after 11 days without sleep he suffered no hallucinations or paranoia and no psychotic symptoms. But Coren challenges this often repeated fact in his book. Coren describes the day-by-day impact on Randy, as documented by John Ross of the US Navy Medical europsychiatric Research Unit in San Diego. Randy had trouble focusing his eyes on day 2, hallucinations on day 4, and slurred speech and a short attention span by the last day.
Certainly there are drugs such as caffeine, cocaine and amphetamines that keep you awake, but these cannot sustain you for very long.
A google search on sleep deprivation yields many links to sites that cover this subject.
Helen Chrisp asks: why does lack of sleep play with your brain?
This is just speculation, but the need for sleep appears to be due, in part, to a compound known as adenosine. This natural chemical builds up in your blood as time awake increases. While you sleep, your body breaks down the adenosine. Thus, this molecule may be what your body uses to keep track of lost sleep and to trigger sleep when needed. An accumulation of adenosine and other factors might explain why, after several nights of less than optimal amounts of sleep, you build up a sleep debt that you must make up by sleeping longer than normal. Because of such built-in molecular feedback, you can't adapt to getting less sleep than your body needs. Eventually, a lack of sleep catches up with you.
There may be quite a few other factors involved, but sleep and the need for sleep is one of the greatest mysteries of science. Nobody knows why we need to sleep.