According to Scientific American, the world record for the longest period without sleep goes to a high school student who stayed awake for 11 days in the 1960s as part of a science fair project. Sleep deprivation causes cognitive deficits in humans, though the deficits are easily reversed with sleep.
Wikipedia says that individuals suffering from fatal familial insomnia or FFI go months or even years without experiencing REM sleep, which is crucial for the body to repair itself. Instead, these individuals stay at stage 1 sleep, which is the lightest sleep stage. The condition is always fatal and taking sleep aids may actually hasten the progression of the disease.