Actually, it is possible to directly die from a lack of sleep, although it's rare for humans to do so.
Sleep is necessary for resetting the chemical balance of the brain, and going for too long will be fatal - some (rather sadistic) tests on lab mice showed that it only takes about a week or so of no sleep to kill mice.
Humans, however, have a special function where they take "micro-naps" that allow parts of the brain to be shut off for small periods of time, allowing a minor reset of brain chemicals, and greatly extending the time it's technically possible to go completely without sleep without actually dying. These micro-naps are the cause of people who are sleep deprived having moments of spacing out - they're actually sleeping for a few seconds at a time with their eyes open.
Even with micro-naps, people will suffer brain damage and eventually die from lack of sleep from not getting real sleep for a few months, however, obviously, nobody would normally do such a thing voluntarily, and you pretty much only see anything like that in something like a torture program.
