That's how long Randy Gardner, then a 17-year-old high school student, stayed awake in 1965 for a scientific experiment on sleep deprivation. To be more exact, he stayed awake for 264 hours.
Considering that he's still alive and healthy today, this didn't seem to have any long-term, negative health consequences.
Others have tried to stay up longer and beat the record, and some claim to have done so, but as far as I know, none of these claims have been validated, and Randy remains the record-holder.
In truth, this is just the longest someone has stayed awake. It doesn't mean that's the absolute maximum that a person could live without sleep.
But no one has gone longer than that and survived to tell the tale!