Sleep deprivation isn't always obvious.

"Sleep debt" (or sleep deficit) is the difference between the amount of sleep you should be getting and the amount you actually get. This difference represents a deficit which increases every time we skim some extra minutes off our nightly sleep.
"People accumulate sleep debt surreptitiously," says psychiatrist William C. Dement, founder of the Stanford University Sleep Clinic. In fact, studies have shown that such short-term sleep deprivation leads to a "foggy brain", worsened vision, impaired driving and problems in short-term memory. Long-term effects include obesity, insulin resistance, and heart disease.
And most Americans suffer from chronic deprivation. A 2005 survey by the National Sleep Foundation reports that, on average, Americans sleep 6.9 hours per night -6.8 hours during the week and 7.4 hours on the weekends: experts recommend eight hours of sleep per night.
The problem is that after a long period of sleep deprivation, you stop realizing how tired you actually are.

In a study by the University of Pennsylvania School of Medicine, researchers followed three groups of subjects for 14 days; one group slept for eight hours a night, the second group slept for six hours a night, and the third group slept just four hours a night. Cognitive tests after the two-week period showed that the people with only six hours of sleep a night showed similar reaction times as people with a blood alcohol content of 0.1 percent; a level which is considered legally impaired.

Other studies have indicated that a consistent lack of sleep may cause permanent damage to your brain. 
One in particular, also conducted by the University of Pennsylvania School of Medicine and published in The Journal of Neuroscience looked at lab mice that were kept awake to replicate the kind of sleep loss common in modern life, through night shifts or long hours in the office.
The team studied certain brain cells which are involved in keeping the brain alert. After several days of sleep patterns similar to those followed by night workers - three days of night shifts with only four to five hours sleep in 24 hours - the mice lost 25% of the brain cells in vital parts of the brain stem.

After only a night or two of sleep deficit, a few nights of adequate sleep are usually enough to reverse the effects and "recharge" your system. But chronic sleep deprivation may be harder to recover from.
For information on how to increase your sleep drive and improve your waking hours, take a look at our  sleep hygiene recommendations. If you have a problem with daytime sleepiness and you have increased your sleep length without improving your daytime sleepiness, then you should be evaluated by a Sleep Disorders Specialist. With proper care most people can obtain the treatment they need to improve this problem.

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References:
Sleep-Deprived People Can’t Tell They’re Sleep-Deprived; Melissa Dahl, NYMag.com
Lost sleep leads to loss of brain cells, study suggests; Helen Briggs, BBC News