Actually there's a mental disorder which kills you by sleep deprivation. You sleep less and less, then you snuff it.
On a related note, lack of sleep leads to severe chemical changes in the brain, ususally triggering psychosis.
Sleep deprivation also aggravates any EXISTING mental problems, ie ADHD, schizophrenia, etc. It messes with your genetic structure (bits stop working), all your systems slow down (immune system for example), and it slashes your life expectancy. Nearly all experiments end up with the rapid death of the test subject. As far as I can find, the longest amount of time a person stayed awake was ELEVEN DAYS, and that was a Stanford experiment. He slept for over 14 hours afterward. He suffered a few hallucinations but nothing else.
I would however caution that he's probably the exception rather than the rule.
Edit - NATURALLY, every test subject would finally collapse due to the increasing strain on the body, however lab test subjects have a gene altered so that they are physically incapable of sleep.